In NEW JERSEY, once a seller accepts an offer and it is in attorney review, if they put in writing, that all subsequent offers are for back-up only, you can still present an offer. But this means just what it says, that if the accepted offer falls apart, the seller can go back to their "back-ups" and see if the other buyers are still interested.
I as I said before, if the seller HAS NOT put in writing that subsequent offers are for back-up only (or that they are not accepting any other offers at all), TECHNICALLY you can submit an offer right up to the day of closing.
However, in both cases, it still doesn't mean that they will accept your offer. Additionally once the offer they have is out of attorney review and "under contract", the seller can face some penalties if they cancel the previous offer and take yours, so it's highly unlikey they would.