Yes. In this situation, the second offer, once accepted, can be a back-up contract only. According to Paragraph B of the Addendum for Sale of Other Property by Buyer (TXR 1908, TREC 10-6), the seller may not compel the first buyer to waive the contingency or terminate the contract under the addendum until the seller accepts a written offer to sell the property.
The seller may not accept a second offer unless the back-up addendum is part of the second offer. Otherwise, the seller may be obligated to sell to two different buyers, especially if the first buyer waives the contingency.
