Local customs vary from court to court and DA's office to DA's office. The DA can make you fifty plea offers if they want, even right up to trial. There's no guarantee though. If they make an offer, your attorney is legally bound to convey it to you and discuss it so you can make a decision. I wouldn't play games with waiting to see if there's a third and final offer - it may never come or it may be worse. If the case is stacking up against you and you're offered a deal that sounds reasonable, discuss that offer with your attorney. If they think they can get a better deal, discuss that as well.
Always assume the offer is what it is - and be ready to accept that if you turn it down, you may never get it back.