One at a time could still work ... if your agent is familiar with bank owned homes and the quirks of different lenders (what they tend to accept, for example) it could help a great deal.
It can be done, but I would be extra careful when I do that. There is normally an experiation on your offer, and make sure you understand the dates and conditions in the contracts. You just don't want to be accepted in two offers. There is an inspection period where you typically can backout of contract if you changed your mind. Also, I dont know if many people will know that you put in more than one offer, but it's always good to make sure all rules are followed so you don't lose your deposit.