If the house is bank owned then typically the listing agent y will stop accepting offers once the bank makes a counter offer on one of them. If the house is in foreclosure and is subject to a short sale then the listing agent may look at offers until the bank accepts the offer which can be a long time. Under normal circumstances, if the listing agent has accepted an offer subject to inspection, it would most likely close and you're out of luck as far as that house is concerned. Dealing with bank mediated tranasctions in today's market, however, it seems that anything can happen. I would recommend that if you find that you like the house and really want it, to write a back up offer so in the event the other offer falls through you can be next in line. There are a number of ways to give yourself an advantage in multiple offer situations, however out bidding the accepted offer isn't one of them. Hopefully your agent has experience with this type of transaction since often times it's more complex than a traditional transaction.