Depending on your local MLS rules, the status of the listing would be changed to "pending, show for back ups" or something similar if the homeowner/seller has accepted an offer, and is looking for other offers as back ups.
If this is a short sale, and the seller is open to looking at and receiving other offers, then the seller can accept subsequent offers as back ups...all offers are forwarded to the Lender who makes the final decision. No offer is really accepted until the lender accepts it.
So if your offer was accepted by the Seller as being in the primary position, the listing agent would change the status (in our local MLS, it's 24 hours from the acceptance by the seller). BUT remember that if another offer is stronger or better, in the opinion of the lender, the lender can choose to accept that offer instead.
Price alone doesn't dictate the strength of an offer. You should factor in the terms: large initial deposit, large down payment, shorter time to do inspections, all cash offer, no contingencies, no credits requested, AS IS purchase, etc. are all gauges of strength.
And how would you know your offer is the strongest? Who told you? Again, it's the lender who makes the final decision. It's not the seller or the listing agent.