how to add new data to existing map in firebase flutter

Question

here is the firebase document data

I want to add a new map value to the purchased-id. this is the current code

FirebaseFirestore.instance.collection('users').doc(userID).set({
  'purchased-id': {
    widget.head: widget.id,
  }
});               

but with this code the map value is replaced, how do I add another map value to the existing map

like this