Running a eBay style auction store on a Squarespace site instead of linking to eBay.

Has anyone found a solution to add a eBay-style bidding option for purchases in a store? I linked our current setup, but the links then take you to eBay where the bidding all happens. I would love to find something to keep it all in-house and not take buyers to another website to engage. I have found multiple companies that host auctions, but it would effectively be the same scenario, the customer would click a link  and it would take them to the other company's site.