Yes, you can make offers on more than one house at a time--as long as you are prepared to buy all of them (or at least all of the ones where your offer is accepted). There is NO right to withdraw one accepted offer or get out of the contract created by the acceptance because some other offer was accepted. The seller could sue the buyer to enforce the contract and recover any amounts they lose due to the withdrawal, such as:1) If the next best offer that ends up buying the home is $10k less, the seller could sue for the $10k;2) If after this offer is withdrawn, it takes an extra 2 weeks to sell the house, the seller could get two weeks of carrying costs;3) If the seller spent money on this offer (e.g. hired  a lawyer to look at the offer), the seller could recover that cost.However, the law only provides compensation to the extent someone is injured, damaged, or loses money. If the seller comes out even or ahead (e.g. promptly sold the house for as much or more than the withdrawn offer), there'd be no point in suing, since not having suffered a loss, the seller would not be entitled to compensation.