From the Sellers points...there should not be a problem when a Buyer wants to revise the offer to higher price. I am assuming that you have a fully executed contract with the Seller contingent on the Seller's lender approval. Therefore, one way to revise your offer without opening the existing contract could be through an addendum to the contract whereby the parties agree to ammend the purchase price but leave all other terms unchanged. Contact your Realtor as soon as possible so that they can assist you in doing this. Time is very important if the Sellers lender is reviewing the offers on the table and is about to make a decision.
Now, it should be noted that while the highest purchase price offer may appear best on its face, it may not always be the one the Seller (or Seller's Lender) goes with. It is possible that a higher purchase price will in fact net the Seller less if there are Seller contributions involved. There are also other terms of the offer to be considered (besides price) that may affect a seller's lender decision.
Concerning your qestion: "If we do revise the offer, will the bank try to get more money from us then?" The bank can always try to get more money (and they usually do), but it is up to you to accept their terms or not. Be careful not to get caught up in the heat of the moment and try to use your best judgment so that you make a decision that you will be happy with for years to come. Good Luck!!!
It would not be fair to the current "best" offer to allow another buyer to come in and override their offer without allowing them an opportunity to increase theirs as well. Do you see where this is going? It doesn't really end fairly.
Unfortunately, short sales are new to most agents, and the majority of agents who take them on don't have enough daily experience in them to set up appropriate processes to safeguard the transaction.
I would recommend you look for another property and have your agent do a little more investigating of the listing agent's experience and process prior to making an offer.
Different agents feel differently about this, but I feel that it is my job to make it work for my sellers.
So, you can try and see what it would take, and then put in a higher offer if the listing agent will do it.