First, understand that it is quite common for there to be multiple offers at one time--even if a property has been on the market for months. There comes a moment when it is the "deal of the day" because competing homes have been sold or withdrawn.
In addition to standing firm on your price, you can add an Expiration Date/Time to your offer. This keeps the other side from using your offer as leverage with other potential buyers. An alternative is for your agent to tell the listing agent that although you did not put an expiration on your offer, you have the right to call your agent at any time and instruct him/her to withdraw the offer.
Your agent should remind the other agent of this, along with asking the listing agent to let the Seller know how this works. Sample wording might be, "Make sure the Seller understands that if the Buyer tells me to withdraw the offer, it's over--immediately. There is no opportunity for the Seller to come back with a response. And if all the parties do this, the Seller is left with NO offers. So, make sure the Seller is aware of this potential situation."
Generally, you will not know the terms of the other offer(s). This is a way to "smoke them out". If they are dealing with an inferior offer, they will be interested in keeping you on the hook. If it is a better offer than yours, then you probably would not have won the bidding contest, anyway. Even if you really want the house, don't get pulled into paying too much for it!