From a recent Business Week article, here are some suggested possibilities:
Banks may be able to finance the sale of their own troubled loans, lending money to the public-private partnerships that buy the assets. A bank's loan to the partnership would be buttressed by an FDIC guarantee. Administration officials confirm that the Treasury may allow such seller financing. The move essentially replaces junky mortgages on the bank's books with an FDIC-guaranteed loan.
…Say a private investor in one of the partnerships owns big stockholdings in a bank putting assets out to auction. By overbidding for the bank's sludge loans, the investor could help drive up the banks' shares and make a tidy profit.
…Perhaps the most intricate maneuvers will likely stem from "layering" the government's many programs of the last six months. Starting with some of the capital infusion received last fall from the Treasury, a bank could invest in a private partnership that buys toxic assets using a loan guaranteed by the FDIC. Those assets could then be chopped up and sold as securities to other investors–who put together the financing for the deal by availing themselves of another program of low-risk loans from the Federal Reserve. Thus the original bank's capital at risk in this web of deals would be almost nil. "[This] is going right back to the practices that got us into this problem–except using government leverage," Young says. "It might lead to an even wilder party than we saw before."
You should not assume that all of these strategies will be legally possible or that they necessarily work. Furthermore the greater danger may be that banks are afraid to make money in a partnership with government aid, for political reasons. Still, if you are seeking to think through possible problems in the Geithner plan, the article is a one good place to start.
Ricardo Caballero's defense of the Geithner plan is here.
Addendum: Jeff Sachs is worried.