diff --git a/src/systems/abstractsystem.jl b/src/systems/abstractsystem.jl
index d91659c0d7..aa02a5fb73 100644
--- a/src/systems/abstractsystem.jl
+++ b/src/systems/abstractsystem.jl
@@ -3090,7 +3090,7 @@ function process_parameter_dependencies(pdeps, ps)
                  end
                  for p in pdeps]
     end
-    lhss = BasicSymbolic[]
+    lhss = []
     for p in pdeps
         if !isparameter(p.lhs)
             error("LHS of parameter dependency must be a single parameter. Found $(p.lhs).")
@@ -3101,6 +3101,7 @@ function process_parameter_dependencies(pdeps, ps)
         end
         push!(lhss, p.lhs)
     end
+    lhss = map(identity, lhss)
     pdeps = topsort_equations(pdeps, union(ps, lhss))
     ps = filter(ps) do p
         !any(isequal(p), lhss)
diff --git a/src/systems/index_cache.jl b/src/systems/index_cache.jl
index 90ca3eb781..00f7837407 100644
--- a/src/systems/index_cache.jl
+++ b/src/systems/index_cache.jl
@@ -49,7 +49,7 @@ struct IndexCache
     constant_idx::ParamIndexMap
     nonnumeric_idx::NonnumericMap
     observed_syms::Set{BasicSymbolic}
-    dependent_pars::Set{BasicSymbolic}
+    dependent_pars::Set{Union{BasicSymbolic, CallWithMetadata}}
     discrete_buffer_sizes::Vector{Vector{BufferTemplate}}
     tunable_buffer_size::BufferTemplate
     constant_buffer_sizes::Vector{BufferTemplate}
@@ -275,7 +275,8 @@ function IndexCache(sys::AbstractSystem)
         end
     end
 
-    dependent_pars = Set{BasicSymbolic}()
+    dependent_pars = Set{Union{BasicSymbolic, CallWithMetadata}}()
+
     for eq in parameter_dependencies(sys)
         sym = eq.lhs
         ttsym = default_toterm(sym)
diff --git a/test/parameter_dependencies.jl b/test/parameter_dependencies.jl
index 034c27041e..9cfd4ca5c5 100644
--- a/test/parameter_dependencies.jl
+++ b/test/parameter_dependencies.jl
@@ -177,6 +177,29 @@ end
     @test SciMLBase.successful_retcode(sol)
 end
 
+struct CallableFoo
+    p::Any
+end
+
+@register_symbolic CallableFoo(x)
+
+(f::CallableFoo)(x) = f.p + x
+
+@testset "callable parameters" begin
+    @variables y(t) = 1
+    @parameters p=2 (i::CallableFoo)(..)
+
+    eqs = [D(y) ~ i(t) + p]
+    @named model = ODESystem(eqs, t, [y], [p, i];
+        parameter_dependencies = [i ~ CallableFoo(p)])
+    sys = structural_simplify(model)
+
+    prob = ODEProblem(sys, [], (0.0, 1.0))
+    sol = solve(prob, Tsit5())
+
+    @test SciMLBase.successful_retcode(sol)
+end
+
 @testset "Clock system" begin
     dt = 0.1
     @variables x(t) y(t) u(t) yd(t) ud(t) r(t) z(t)