diff --git a/docs/src/API/codegen.md b/docs/src/API/codegen.md
index 4f31405174..0092e1cb8e 100644
--- a/docs/src/API/codegen.md
+++ b/docs/src/API/codegen.md
@@ -50,5 +50,5 @@ ModelingToolkit.calculate_A_b
 All code generation eventually calls `build_function_wrapper`.
 
 ```@docs
-build_function_wrapper
+ModelingToolkit.build_function_wrapper
 ```
diff --git a/src/systems/diffeqs/basic_transformations.jl b/src/systems/diffeqs/basic_transformations.jl
index f823260e2a..200e0d3d56 100644
--- a/src/systems/diffeqs/basic_transformations.jl
+++ b/src/systems/diffeqs/basic_transformations.jl
@@ -1037,9 +1037,11 @@ function respecialize(sys::AbstractSystem, mapping; all = false)
         """
 
         if iscall(k)
-            op = operation(k)
+            op = operation(k)::BasicSymbolic
+            @assert !iscall(op)
+            op = SymbolicUtils.Sym{SymbolicUtils.FnType{Tuple{Any}, T}}(nameof(op))
             args = arguments(k)
-            new_p = SymbolicUtils.term(op, args...; type = T)
+            new_p = op(args...)
         else
             new_p = SymbolicUtils.Sym{T}(getname(k))
         end
diff --git a/src/systems/parameter_buffer.jl b/src/systems/parameter_buffer.jl
index 637ed674ae..f91348d0c9 100644
--- a/src/systems/parameter_buffer.jl
+++ b/src/systems/parameter_buffer.jl
@@ -763,8 +763,14 @@ function __remake_buffer(indp, oldbuf::MTKParameters, idxs, vals; validate = tru
         oldbuf.discrete, newbuf.discrete)
     @set! newbuf.constant = narrow_buffer_type_and_fallback_undefs.(
         oldbuf.constant, newbuf.constant)
-    @set! newbuf.nonnumeric = narrow_buffer_type_and_fallback_undefs.(
-        oldbuf.nonnumeric, newbuf.nonnumeric)
+    for (oldv, newv) in zip(oldbuf.nonnumeric, newbuf.nonnumeric)
+        for i in eachindex(oldv)
+            isassigned(newv, i) && continue
+            newv[i] = oldv[i]
+        end
+    end
+    @set! newbuf.nonnumeric = Tuple(
+        typeof(oldv)(newv) for (oldv, newv) in zip(oldbuf.nonnumeric, newbuf.nonnumeric))
     if !ArrayInterface.ismutable(oldbuf)
         @set! newbuf.tunable = similar_type(oldbuf.tunable, eltype(newbuf.tunable))(newbuf.tunable)
         @set! newbuf.initials = similar_type(oldbuf.initials, eltype(newbuf.initials))(newbuf.initials)
diff --git a/src/systems/problem_utils.jl b/src/systems/problem_utils.jl
index 2a1208586b..2f5db01479 100644
--- a/src/systems/problem_utils.jl
+++ b/src/systems/problem_utils.jl
@@ -701,9 +701,10 @@ function.
 Note that the getter ONLY works for problem-like objects, since it generates an observed
 function. It does NOT work for solutions.
 """
-Base.@nospecializeinfer function concrete_getu(indp, syms::AbstractVector)
+Base.@nospecializeinfer function concrete_getu(indp, syms; eval_expression, eval_module)
     @nospecialize
-    obsfn = build_explicit_observed_function(indp, syms; wrap_delays = false)
+    obsfn = build_explicit_observed_function(
+        indp, syms; wrap_delays = false, eval_expression, eval_module)
     return ObservedWrapper{is_time_dependent(indp)}(obsfn)
 end
 
@@ -757,7 +758,8 @@ takes a value provider of `srcsys` and a value provider of `dstsys` and returns
 - `p_constructor`: The `p_constructor` argument to `process_SciMLProblem`.
 """
 function get_mtkparameters_reconstructor(srcsys::AbstractSystem, dstsys::AbstractSystem;
-        initials = false, unwrap_initials = false, p_constructor = identity)
+        initials = false, unwrap_initials = false, p_constructor = identity,
+        eval_expression = false, eval_module = @__MODULE__)
     _p_constructor = p_constructor
     p_constructor = PConstructorApplicator(p_constructor)
     # if we call `getu` on this (and it were able to handle empty tuples) we get the
@@ -773,7 +775,7 @@ function get_mtkparameters_reconstructor(srcsys::AbstractSystem, dstsys::Abstrac
     tunable_getter = if isempty(tunable_syms)
         Returns(SizedVector{0, Float64}())
     else
-        p_constructor ∘ concrete_getu(srcsys, tunable_syms)
+        p_constructor ∘ concrete_getu(srcsys, tunable_syms; eval_expression, eval_module)
     end
     initials_getter = if initials && !isempty(syms[2])
         initsyms = Vector{Any}(syms[2])
@@ -792,7 +794,7 @@ function get_mtkparameters_reconstructor(srcsys::AbstractSystem, dstsys::Abstrac
                 end
             end
         end
-        p_constructor ∘ concrete_getu(srcsys, initsyms)
+        p_constructor ∘ concrete_getu(srcsys, initsyms; eval_expression, eval_module)
     else
         Returns(SizedVector{0, Float64}())
     end
@@ -810,7 +812,7 @@ function get_mtkparameters_reconstructor(srcsys::AbstractSystem, dstsys::Abstrac
         # tuple of `BlockedArray`s
         Base.Fix2(Broadcast.BroadcastFunction(BlockedArray), blockarrsizes) ∘
         Base.Fix1(broadcast, p_constructor) ∘
-        getu(srcsys, syms[3])
+        concrete_getu(srcsys, syms[3]; eval_expression, eval_module)
     end
     const_getter = if syms[4] == ()
         Returns(())
@@ -826,7 +828,8 @@ function get_mtkparameters_reconstructor(srcsys::AbstractSystem, dstsys::Abstrac
         end)
         # nonnumerics retain the assigned buffer type without narrowing
         Base.Fix1(broadcast, _p_constructor) ∘
-        Base.Fix1(Broadcast.BroadcastFunction(call), buftypes) ∘ getu(srcsys, syms[5])
+        Base.Fix1(Broadcast.BroadcastFunction(call), buftypes) ∘
+        concrete_getu(srcsys, syms[5]; eval_expression, eval_module)
     end
     getters = (
         tunable_getter, initials_getter, discs_getter, const_getter, nonnumeric_getter)
@@ -853,14 +856,19 @@ Construct a `ReconstructInitializeprob` which reconstructs the `u0` and `p` of `
 with values from `srcsys`.
 """
 function ReconstructInitializeprob(
-        srcsys::AbstractSystem, dstsys::AbstractSystem; u0_constructor = identity, p_constructor = identity)
+        srcsys::AbstractSystem, dstsys::AbstractSystem; u0_constructor = identity, p_constructor = identity,
+        eval_expression = false, eval_module = @__MODULE__)
     @assert is_initializesystem(dstsys)
-    ugetter = u0_constructor ∘ getu(srcsys, unknowns(dstsys))
+    ugetter = u0_constructor ∘
+              concrete_getu(srcsys, unknowns(dstsys); eval_expression, eval_module)
     if is_split(dstsys)
-        pgetter = get_mtkparameters_reconstructor(srcsys, dstsys; p_constructor)
+        pgetter = get_mtkparameters_reconstructor(
+            srcsys, dstsys; p_constructor, eval_expression, eval_module)
     else
         syms = parameters(dstsys)
-        pgetter = let inner = concrete_getu(srcsys, syms), p_constructor = p_constructor
+        pgetter = let inner = concrete_getu(srcsys, syms; eval_expression, eval_module),
+            p_constructor = p_constructor
+
             function _getter2(valp, initprob)
                 p_constructor(inner(valp))
             end
@@ -924,18 +932,20 @@ Given `sys` and its corresponding initialization system `initsys`, return the
 `initializeprobpmap` function in `OverrideInitData` for the systems.
 """
 function construct_initializeprobpmap(
-        sys::AbstractSystem, initsys::AbstractSystem; p_constructor = identity)
+        sys::AbstractSystem, initsys::AbstractSystem; p_constructor = identity, eval_expression, eval_module)
     @assert is_initializesystem(initsys)
     if is_split(sys)
         return let getter = get_mtkparameters_reconstructor(
-                initsys, sys; initials = true, unwrap_initials = true, p_constructor)
+                initsys, sys; initials = true, unwrap_initials = true, p_constructor,
+                eval_expression, eval_module)
             function initprobpmap_split(prob, initsol)
                 getter(initsol, prob)
             end
         end
     else
-        return let getter = getu(initsys, parameters(sys; initial_parameters = true)),
-            p_constructor = p_constructor
+        return let getter = concrete_getu(
+                initsys, parameters(sys; initial_parameters = true);
+                eval_expression, eval_module), p_constructor = p_constructor
 
             function initprobpmap_nosplit(prob, initsol)
                 return p_constructor(getter(initsol))
@@ -1039,14 +1049,14 @@ struct GetUpdatedU0{GG, GIU}
     get_initial_unknowns::GIU
 end
 
-function GetUpdatedU0(sys::AbstractSystem, initsys::AbstractSystem, op::AbstractDict)
+function GetUpdatedU0(sys::AbstractSystem, initprob::SciMLBase.AbstractNonlinearProblem, op::AbstractDict)
     dvs = unknowns(sys)
     eqs = equations(sys)
     guessvars = trues(length(dvs))
     for (i, var) in enumerate(dvs)
         guessvars[i] = !isequal(get(op, var, nothing), Initial(var))
     end
-    get_guessvars = getu(initsys, dvs[guessvars])
+    get_guessvars = getu(initprob, dvs[guessvars])
     get_initial_unknowns = getu(sys, Initial.(dvs))
     return GetUpdatedU0(guessvars, get_guessvars, get_initial_unknowns)
 end
@@ -1108,7 +1118,7 @@ function maybe_build_initialization_problem(
         guesses, missing_unknowns; implicit_dae = false,
         time_dependent_init = is_time_dependent(sys), u0_constructor = identity,
         p_constructor = identity, floatT = Float64, initialization_eqs = [],
-        use_scc = true, kwargs...)
+        use_scc = true, eval_expression = false, eval_module = @__MODULE__, kwargs...)
     guesses = merge(ModelingToolkit.guesses(sys), todict(guesses))
 
     if t === nothing && is_time_dependent(sys)
@@ -1117,7 +1127,7 @@ function maybe_build_initialization_problem(
 
     initializeprob = ModelingToolkit.InitializationProblem{iip}(
         sys, t, op; guesses, time_dependent_init, initialization_eqs,
-        use_scc, u0_constructor, p_constructor, kwargs...)
+        use_scc, u0_constructor, p_constructor, eval_expression, eval_module, kwargs...)
     if state_values(initializeprob) !== nothing
         _u0 = state_values(initializeprob)
         if ArrayInterface.ismutable(_u0)
@@ -1145,7 +1155,7 @@ function maybe_build_initialization_problem(
     initializeprob = remake(initializeprob; p = initp)
 
     get_initial_unknowns = if time_dependent_init
-        GetUpdatedU0(sys, initializeprob.f.sys, op)
+        GetUpdatedU0(sys, initializeprob, op)
     else
         nothing
     end
@@ -1153,7 +1163,8 @@ function maybe_build_initialization_problem(
         copy(op), copy(guesses), Vector{Equation}(initialization_eqs),
         use_scc, time_dependent_init,
         ReconstructInitializeprob(
-            sys, initializeprob.f.sys; u0_constructor, p_constructor),
+            sys, initializeprob.f.sys; u0_constructor,
+            p_constructor, eval_expression, eval_module),
         get_initial_unknowns, SetInitialUnknowns(sys))
 
     if time_dependent_init
@@ -1172,10 +1183,9 @@ function maybe_build_initialization_problem(
         initializeprobpmap = nothing
     else
         initializeprobpmap = construct_initializeprobpmap(
-            sys, initializeprob.f.sys; p_constructor)
+            sys, initializeprob.f.sys; p_constructor, eval_expression, eval_module)
     end
 
-    reqd_syms = parameter_symbols(initializeprob)
     # we still want the `initialization_data` because it helps with `remake`
     if initializeprobmap === nothing && initializeprobpmap === nothing
         update_initializeprob! = nothing
@@ -1186,7 +1196,9 @@ function maybe_build_initialization_problem(
     filter!(punknowns) do p
         is_parameter_solvable(p, op, defs, guesses) && get(op, p, missing) === missing
     end
-    pvals = getu(initializeprob, punknowns)(initializeprob)
+    # See comment below for why `getu` is not used here.
+    _pgetter = build_explicit_observed_function(initializeprob.f.sys, punknowns)
+    pvals = _pgetter(state_values(initializeprob), parameter_values(initializeprob))
     for (p, pval) in zip(punknowns, pvals)
         p = unwrap(p)
         op[p] = pval
@@ -1198,7 +1210,13 @@ function maybe_build_initialization_problem(
     end
 
     if time_dependent_init
-        uvals = getu(initializeprob, collect(missing_unknowns))(initializeprob)
+        # We can't use `getu` here because that goes to `SII.observed`, which goes to
+        # `ObservedFunctionCache` which uses `eval_expression` and `eval_module`. If
+        # `eval_expression == true`, this then runs into world-age issues. Building an
+        # RGF here is fine since it is always discarded. We can't use `eval_module` for
+        # the RGF since the user may not have run RGF's init.
+        _ugetter = build_explicit_observed_function(initializeprob.f.sys, collect(missing_unknowns))
+        uvals = _ugetter(state_values(initializeprob), parameter_values(initializeprob))
         for (v, val) in zip(missing_unknowns, uvals)
             op[v] = val
         end
@@ -1461,7 +1479,7 @@ function process_SciMLProblem(
         if is_time_dependent(sys) && t0 === nothing
             t0 = zero(floatT)
         end
-        initialization_data = SciMLBase.remake_initialization_data(
+        initialization_data = @invokelatest SciMLBase.remake_initialization_data(
             sys, kwargs, u0, t0, p, u0, p)
         kwargs = merge(kwargs, (; initialization_data))
     end
@@ -1773,7 +1791,8 @@ Construct SciMLProblem `T` with positional arguments `args` and keywords `kwargs
 """
 function maybe_codegen_scimlproblem(::Type{Val{false}}, T, args::NamedTuple; kwargs...)
     # Call `remake` so it runs initialization if it is trivial
-    remake(T(args...; kwargs...))
+    # Use `@invokelatest` to avoid world-age issues with `eval_expression = true`
+    @invokelatest remake(T(args...; kwargs...))
 end
 
 """
diff --git a/test/basic_transformations.jl b/test/basic_transformations.jl
index dc9d71f300..19899aa50f 100644
--- a/test/basic_transformations.jl
+++ b/test/basic_transformations.jl
@@ -340,11 +340,12 @@ foofn(x) = 4
 
 @testset "`respecialize`" begin
     @parameters p::AbstractFoo p2(t)::AbstractFoo = p q[1:2]::AbstractFoo r
-    rp,
-    rp2 = let
-        only(@parameters p::Bar),
-        SymbolicUtils.term(operation(p2), arguments(p2)...; type = Baz)
-    end
+    rp = only(let p = nothing
+        @parameters p::Bar
+    end)
+    rp2 = only(let p2 = nothing
+        @parameters p2(t)::Baz
+    end)
     @variables x(t) = 1.0
     @named sys1 = System([D(x) ~ foofn(p) + foofn(p2) + x], t, [x], [p, p2, q, r])
 
diff --git a/test/mtkparameters.jl b/test/mtkparameters.jl
index 28ab3759ef..08beb7ed53 100644
--- a/test/mtkparameters.jl
+++ b/test/mtkparameters.jl
@@ -357,7 +357,7 @@ ps = MTKParameters(
     (BlockedArray([1.0, 2.0, 3.0, 4.0, 5.0, 6.0], [3, 3]),
         BlockedArray(falses(1), [1, 0])),
     (), (), ())
-@test SciMLBase.get_saveable_values(sys, ps, 1).x isa Tuple{Vector{Float64}, Vector{Bool}}
+@test SciMLBase.get_saveable_values(sys, ps, 1).x isa Tuple{Vector{Float64}, BitVector}
 tsidx1 = 1
 tsidx2 = 2
 @test length(ps.discrete[1][Block(tsidx1)]) == 3
@@ -368,3 +368,14 @@ with_updated_parameter_timeseries_values(
     sys, ps, tsidx1 => ModelingToolkit.NestedGetIndex(([10.0, 11.0, 12.0], [false])))
 @test ps.discrete[1][Block(tsidx1)] == [10.0, 11.0, 12.0]
 @test ps.discrete[2][Block(tsidx1)][] == false
+
+@testset "Avoid specialization of nonnumeric parameters on `remake_buffer`" begin
+    @variables x(t)
+    @parameters p::Any
+    @named sys = System(D(x) ~ x, t, [x], [p])
+    sys = complete(sys)
+    ps = MTKParameters(sys, [p => 1.0])
+    @test ps.nonnumeric isa Tuple{Vector{Any}}
+    ps2 = remake_buffer(sys, ps, [p], [:a])
+    @test ps2.nonnumeric isa Tuple{Vector{Any}}
+end
diff --git a/test/precompile_test.jl b/test/precompile_test.jl
index 38051d9d49..6fdc1b5cbf 100644
--- a/test/precompile_test.jl
+++ b/test/precompile_test.jl
@@ -1,5 +1,6 @@
 using Test
 using ModelingToolkit
+using OrdinaryDiffEqDefault
 
 using Distributed
 
@@ -38,3 +39,5 @@ ODEPrecompileTest.f_eval_bad(u, p, 0.1)
 @test parentmodule(typeof(ODEPrecompileTest.f_eval_good.f.f_oop)) ==
       ODEPrecompileTest
 @test ODEPrecompileTest.f_eval_good(u, p, 0.1) == [4, 0, -16]
+
+@test_nowarn solve(ODEPrecompileTest.prob_eval)
diff --git a/test/precompile_test/ODEPrecompileTest.jl b/test/precompile_test/ODEPrecompileTest.jl
index 2111f7ba64..c77c897655 100644
--- a/test/precompile_test/ODEPrecompileTest.jl
+++ b/test/precompile_test/ODEPrecompileTest.jl
@@ -36,4 +36,24 @@ const f_eval_bad = system(; eval_expression = true, eval_module = @__MODULE__)
 # Change the module the eval'd function is eval'd into to be the containing module,
 # which should make it be in the package image
 const f_eval_good = system(; eval_expression = true, eval_module = @__MODULE__)
+
+function problem(; kwargs...)
+    # Define some variables
+    @independent_variables t
+    @parameters σ ρ β
+    @variables x(t) y(t) z(t)
+    D = Differential(t)
+
+    # Define a differential equation
+    eqs = [D(x) ~ σ * (y - x),
+        D(y) ~ x * (ρ - z) - y,
+        D(z) ~ x * y - β * z]
+
+    @named de = System(eqs, t)
+    de = complete(de)
+    return ODEProblem(de, [x => 1, y => 0, z => 0, σ => 10, ρ => 28, β => 8/3], (0.0, 5.0); kwargs...)
+end
+
+const prob_eval = problem(; eval_expression = true, eval_module = @__MODULE__)
+
 end