Something I see happening a lot with projects is this:
Person A is at the project site and in need of a vendor supply, so they put out a call in chat.
Person B is at that type of vendor, so they purchase and post the items on auction.
This sort of teamwork would be greatly facilitated by the ability to post private auctions, possibly with a reduced (or non-existant) final value fee. A private auction system would also make me more willing to go out and harvest for a partner who is - say - making blocks at the project site, because it would eliminate the possibility that someone would buy up all the materials I'm posting and then re-post them at greatly inflated prices.
Although I'd like to see private auctions available to all players, this could also potentially be used as a subscriber-perk, where both the auctioner and auctionee would need to be subscribers.