No counteroffer. Here was my bidding history $100 on 3.5* on Copley Square - Theatre District : Fail Add 4* on Copley and up bid to $125: Fail Add Brighton - Brookline (no 3.5*) and up bid to $135: Success I did this at the last minute. If I had more time I would have gone in smaller bid increments using the free rebids. Good thing about Boston Priceline is that it has five zones without 3.5* stars (Brighton - Brookline, Fenway Park, Medford - Somerville, North Cambridge - Arlington, South Boston) Good luck on your bids.