any advance on
any advance on (something)
1. A phrase used by an auctioneer to try to increase the bids at an auction. $500! Any advance on $500?
2. By extension, a way to ask if something has progressed. Any advance on that project I assigned you last week?
any advance on —?any higher bid than —?
This phrase is said by an auctioneer to elicit a higher bid, and so is used figuratively as a query about general progress in a particular matter.