diff --git a/app/models/form/response.rb b/app/models/form/response.rb
index e0a83228..54cac061 100644
--- a/app/models/form/response.rb
+++ b/app/models/form/response.rb
@@ -40,7 +40,7 @@ def destroyable?
     end
 
     def form_allows_responses?
-      return true if form.try(:allows_responses?)
+      return true if form.try(:allows_responses?) || user_id&.zero?
 
       errors.add(:form, 'does not allow responses')
       false
diff --git a/db/migrate/20250219195453_remove_unique_index_from_form_responses.rb b/db/migrate/20250219195453_remove_unique_index_from_form_responses.rb
new file mode 100644
index 00000000..c5f6a127
--- /dev/null
+++ b/db/migrate/20250219195453_remove_unique_index_from_form_responses.rb
@@ -0,0 +1,22 @@
+class RemoveUniqueIndexFromFormResponses < ActiveRecord::Migration[7.0]
+  def change
+    reversible do |dir|
+      dir.up do
+        remove_index :form_responses, name: 'index_form_responses_on_form_id_and_user_id'
+
+        add_index :form_responses, %i[form_id user_id],
+                  unique: true,
+                  name: 'index_form_responses_on_form_id_and_user_id_partial',
+                  where: 'user_id != 0'
+      end
+
+      dir.down do
+        remove_index :form_responses, name: 'index_form_responses_on_form_id_and_user_id_partial'
+
+        add_index :form_responses, %i[form_id user_id],
+                  unique: true,
+                  name: 'index_form_responses_on_form_id_and_user_id'
+      end
+    end
+  end
+end
diff --git a/db/schema.rb b/db/schema.rb
index f73dab89..12df11b5 100644
--- a/db/schema.rb
+++ b/db/schema.rb
@@ -10,7 +10,7 @@
 #
 # It's strongly recommended that you check this file into your version control system.
 
-ActiveRecord::Schema[7.0].define(version: 2025_02_18_204807) do
+ActiveRecord::Schema[7.0].define(version: 2025_02_19_195453) do
   # These are extensions that must be enabled in order to support this database
   enable_extension "plpgsql"
 
@@ -229,7 +229,7 @@
     t.datetime "updated_at", precision: nil, null: false
     t.boolean "completed", default: false, null: false
     t.integer "lock_version"
-    t.index ["form_id", "user_id"], name: "index_form_responses_on_form_id_and_user_id", unique: true
+    t.index ["form_id", "user_id"], name: "index_form_responses_on_form_id_and_user_id_partial", unique: true, where: "(user_id <> 0)"
     t.index ["user_id"], name: "index_form_responses_on_user_id"
   end