Will bank accept an offer slightly below the foreclosure price?

[Haiyang A.]

I'm looking at a bank REO that was foreclosed for $122K, and has been listed at $135K for about two months. I wonder:

(1) if a bank would accept an offer that's at or slightly below it's foreclosed amount (e.g., something like 115K, considering the minor repairs it needs?)

(2) how many offers can one make to the same property in a short time frame (can I try $115K, $120K, $125K, $130K, until it get accepted)?

Any comments would be appreciated!!