I'm not sure if this is like what you are looking for, but I was earlier looking at this demo file for something I was doing, and thought maybe it would be helpful for you and your quest.
You should have another table. One where each record has fields for Client ID and Ad ID. Then adding a Client to an ad means adding a record to that table. And removing a client from an ad means deleting that record.
Thanks David! That worked really well and was completely not anywhere near how I approached solving it. Go figure!