I'm curious...why not ask your Realtor this question?? As Alan said, you can accept a backup offer, but you need to understand exactly what a backup offer is. You cannot just terminate the first offer and accept a better backup offer. The first one needs to fall through first (i.e. if buyer terminates over inspection issues, or can't get loan approval). You're dealing with a complex legal transaction. It would be wise to have a Realtor handling this and advising you.