diff --git a/src/ACSetInterface.jl b/src/ACSetInterface.jl
index e78fda1..41c2c5b 100644
--- a/src/ACSetInterface.jl
+++ b/src/ACSetInterface.jl
@@ -12,6 +12,7 @@ using Tables
 using PrettyTables: pretty_table
 
 using ..ColumnImplementations: AttrVar
+using ..PreimageCaches: is_injective
 
 using ..Schemas: types, attrs, attrtypes
 
@@ -250,6 +251,9 @@ function set_subpart! end
 # Inlined for the same reason as `subpart`.
 
 @inline function set_subpart!(acs::ACSet , parts::Union{AbstractVector{Int}, AbstractSet{Int}}, name, vals)
+  if is_injective(acs.subparts[name])
+    clear_subpart!(acs, parts, name)
+  end
   broadcast(parts, vals) do part, val
     set_subpart!(acs, part, name, val)
   end
diff --git a/src/Columns.jl b/src/Columns.jl
index fd72598..bb0e1ea 100644
--- a/src/Columns.jl
+++ b/src/Columns.jl
@@ -10,7 +10,7 @@ using Reexport
 @reexport using ..PreimageCaches
 
 import ..Mappings: view_with_default
-import ..PreimageCaches: preimage, preimage_multi
+import ..PreimageCaches: preimage, preimage_multi, is_injective
 
 # Columns
 #########
@@ -94,4 +94,6 @@ view_with_default(c::Column, xs, def) = ColumnView(c, xs, def)
 
 Base.size(c::ColumnView) = size(c.indices)
 
+is_injective(c::Column) = is_injective(c.pc)
+
 end
diff --git a/src/PreimageCaches.jl b/src/PreimageCaches.jl
index 205fe8a..7919084 100644
--- a/src/PreimageCaches.jl
+++ b/src/PreimageCaches.jl
@@ -35,6 +35,7 @@ performance implications.
 - [`preimage`](@ref)
 - [`assign!`](@ref)
 - [`unassign!`](@ref)
+- [`is_injective`](@ref) (defaults to false if not implemented)
 """
 abstract type PreimageCache{S,T} end
 
@@ -94,6 +95,14 @@ Remove `x` from the preimage of `y`.
 """
 function unassign! end
 
+"""
+Whether or not the cache imposes an injectivity constraint. (default: false)
+"""
+is_injective(::PreimageCache)::Bool = false
+
+# Caches
+########
+
 """
 The trivial preimage mapping. It just computes preimages on the fly, and the
 operations for updating it are noops
@@ -203,4 +212,6 @@ function unassign!(pc::InjectiveCache{S,T}, y::T, x::S) where {S,T}
   delete!(pc.inverse, y)
 end
 
+is_injective(::InjectiveCache)::Bool = true
+
 end
diff --git a/test/ACSets.jl b/test/ACSets.jl
index 1482e9a..de885dd 100644
--- a/test/ACSets.jl
+++ b/test/ACSets.jl
@@ -425,6 +425,8 @@ for lset_maker in lset_makers
   @test isempty(incident(lset, :foo, :label))
 
   @test_throws Exception set_subpart!(lset, 1, :label, :bar)
+  set_subpart!(lset, :, :label, [:bar, :foo])
+  @test subpart(lset, :, :label) == [:bar, :foo]
 end
 
 SchDecGraph = BasicSchema([:E,:V], [(:src,:E,:V),(:tgt,:E,:V)],