diff --git a/src/systems/index_cache.jl b/src/systems/index_cache.jl
index 1e3490ee69..ab0dd08764 100644
--- a/src/systems/index_cache.jl
+++ b/src/systems/index_cache.jl
@@ -40,10 +40,12 @@ const TunableIndexMap = Dict{BasicSymbolic,
     Union{Int, UnitRange{Int}, Base.ReshapedArray{Int, N, UnitRange{Int}} where {N}}}
 const TimeseriesSetType = Set{Union{ContinuousTimeseries, Int}}
 
+const SymbolicParam = Union{BasicSymbolic, CallWithMetadata}
+
 struct IndexCache
     unknown_idx::UnknownIndexMap
     # sym => (bufferidx, idx_in_buffer)
-    discrete_idx::Dict{BasicSymbolic, DiscreteIndex}
+    discrete_idx::Dict{SymbolicParam, DiscreteIndex}
     # sym => (clockidx, idx_in_clockbuffer)
     callback_to_clocks::Dict{Any, Vector{Int}}
     tunable_idx::TunableIndexMap
@@ -56,13 +58,13 @@ struct IndexCache
     tunable_buffer_size::BufferTemplate
     constant_buffer_sizes::Vector{BufferTemplate}
     nonnumeric_buffer_sizes::Vector{BufferTemplate}
-    symbol_to_variable::Dict{Symbol, Union{BasicSymbolic, CallWithMetadata}}
+    symbol_to_variable::Dict{Symbol, SymbolicParam}
 end
 
 function IndexCache(sys::AbstractSystem)
     unks = solved_unknowns(sys)
     unk_idxs = UnknownIndexMap()
-    symbol_to_variable = Dict{Symbol, Union{BasicSymbolic, CallWithMetadata}}()
+    symbol_to_variable = Dict{Symbol, SymbolicParam}()
 
     let idx = 1
         for sym in unks
@@ -95,7 +97,7 @@ function IndexCache(sys::AbstractSystem)
 
     tunable_buffers = Dict{Any, Set{BasicSymbolic}}()
     constant_buffers = Dict{Any, Set{BasicSymbolic}}()
-    nonnumeric_buffers = Dict{Any, Set{Union{BasicSymbolic, CallWithMetadata}}}()
+    nonnumeric_buffers = Dict{Any, Set{SymbolicParam}}()
 
     function insert_by_type!(buffers::Dict{Any, S}, sym, ctype) where {S}
         sym = unwrap(sym)
@@ -103,10 +105,10 @@ function IndexCache(sys::AbstractSystem)
         push!(buf, sym)
     end
 
-    disc_param_callbacks = Dict{BasicSymbolic, Set{Int}}()
+    disc_param_callbacks = Dict{SymbolicParam, Set{Int}}()
     events = vcat(continuous_events(sys), discrete_events(sys))
     for (i, event) in enumerate(events)
-        discs = Set{BasicSymbolic}()
+        discs = Set{SymbolicParam}()
         affs = affects(event)
         if !(affs isa AbstractArray)
             affs = [affs]
@@ -130,26 +132,32 @@ function IndexCache(sys::AbstractSystem)
                isequal(only(arguments(sym)), get_iv(sys))
                 clocks = get!(() -> Set{Int}(), disc_param_callbacks, sym)
                 push!(clocks, i)
-            else
+            elseif is_variable_floatingpoint(sym)
                 insert_by_type!(constant_buffers, sym, symtype(sym))
+            else
+                stype = symtype(sym)
+                if stype <: FnType
+                    stype = fntype_to_function_type(stype)
+                end
+                insert_by_type!(nonnumeric_buffers, sym, stype)
             end
         end
     end
     clock_partitions = unique(collect(values(disc_param_callbacks)))
     disc_symtypes = unique(symtype.(keys(disc_param_callbacks)))
     disc_symtype_idx = Dict(disc_symtypes .=> eachindex(disc_symtypes))
-    disc_syms_by_symtype = [BasicSymbolic[] for _ in disc_symtypes]
+    disc_syms_by_symtype = [SymbolicParam[] for _ in disc_symtypes]
     for sym in keys(disc_param_callbacks)
         push!(disc_syms_by_symtype[disc_symtype_idx[symtype(sym)]], sym)
     end
-    disc_syms_by_symtype_by_partition = [Vector{BasicSymbolic}[] for _ in disc_symtypes]
+    disc_syms_by_symtype_by_partition = [Vector{SymbolicParam}[] for _ in disc_symtypes]
     for (i, buffer) in enumerate(disc_syms_by_symtype)
         for partition in clock_partitions
             push!(disc_syms_by_symtype_by_partition[i],
                 [sym for sym in buffer if disc_param_callbacks[sym] == partition])
         end
     end
-    disc_idxs = Dict{BasicSymbolic, DiscreteIndex}()
+    disc_idxs = Dict{SymbolicParam, DiscreteIndex}()
     callback_to_clocks = Dict{
         Union{SymbolicContinuousCallback, SymbolicDiscreteCallback}, Set{Int}}()
     for (typei, disc_syms_by_partition) in enumerate(disc_syms_by_symtype_by_partition)
@@ -191,6 +199,7 @@ function IndexCache(sys::AbstractSystem)
         end
         haskey(disc_idxs, p) && continue
         haskey(constant_buffers, ctype) && p in constant_buffers[ctype] && continue
+        haskey(nonnumeric_buffers, ctype) && p in nonnumeric_buffers[ctype] && continue
         insert_by_type!(
             if ctype <: Real || ctype <: AbstractArray{<:Real}
                 if istunable(p, true) && Symbolics.shape(p) != Symbolics.Unknown() &&
diff --git a/test/index_cache.jl b/test/index_cache.jl
index c479075797..455203d759 100644
--- a/test/index_cache.jl
+++ b/test/index_cache.jl
@@ -92,3 +92,29 @@ end
     reorder_dimension_by_tunables!(dst, sys, src, [r, q, p]; dim = 2)
     @test dst ≈ stack([vcat(4ones(4), 3ones(3), 1.0) for i in 1:5]; dims = 1)
 end
+
+mutable struct ParamTest
+    y::Any
+end
+(pt::ParamTest)(x) = pt.y - x
+@testset "Issue#3215: Callable discrete parameter" begin
+    function update_affect!(integ, u, p, ctx)
+        integ.p[p.p_1].y = integ.t
+    end
+
+    tp1 = typeof(ParamTest(1))
+    @parameters (p_1::tp1)(..) = ParamTest(1)
+    @variables x(ModelingToolkit.t_nounits) = 0
+
+    event1 = [1.0, 2, 3] => (update_affect!, [], [p_1], [p_1], nothing)
+
+    @named sys = ODESystem([
+            ModelingToolkit.D_nounits(x) ~ p_1(x)
+        ],
+        ModelingToolkit.t_nounits;
+        discrete_events = [event1]
+    )
+    ss = @test_nowarn complete(sys)
+    @test length(parameters(ss)) == 1
+    @test !is_timeseries_parameter(ss, p_1)
+end