I am by far not a data scientist, but I would think it would be in the best interest of the bidder on the whole set to have the individual lots stay as low as possible.
I think both sides should be allowed to increase their own bid during extended bidding.
- The aggregate price goes higher than the high set bid. This notifies everyone who is bidding, including the set bidder.
- The set bidder increases their bid and they are now the high bidder.
- Then it is up to the collective group of individual bidders to bid up the cards, or if they are high bidder to pay a bit more to win their card or loose it.
- The bidders on the individual lots increase their bids, maybe some don't and either they top the set bid or they all loose out.
This gives the advantage to the bidder on the full set as their bid increase can guarantee high bid, however that increase is a much larger amount than what each individual bidder would have to come up with.