I offered the exact asking price listed. Hoever, what are the chances of the bank accepting this offer? Are my chances higher if the home is already empty? Please let me know thanks!

I want to put an offer on a house that’s listed at $80k. The listing agent told our agent that 2 offers have been accepted by the bank already. 1 is obviously a backup offer. 1st offer is $80k. 2nd offer is $80k with 3% closing costs back. If I offered $95k with 6% closing costs, can a bank accept my offer? I thought I read somewhere that in a short sale the bank can always entertain other offers even after accepting others until the house is closed. Is that true?