Often, yes, but you cannot count on it, so lead with terms you can live with. When a seller holds several offers, they generally go one of two directions: ask every buyer to come back with their highest and best, including any terms they are willing to sharpen (price, escrow timeline, contingency periods), or send out a counter at a specific price they want and see who accepts. A seller does not have to treat everyone identically. They can wait to collect all the offers before responding, counter one buyer with a highest-and-best request while countering another at a firm number, and compare what comes back before choosing. So you may well get a second chance to improve your offer, or you may get a single take-it-or-leave-it counter. Because a second round is never promised, go in with your best terms and a clear ceiling already in mind. Knowing your real maximum before the counter comes back keeps you from getting caught up in the moment and agreeing to a number you will regret.