It is possible, but your rights as intended parents are protected through the surrogacy contract, hence the important of signing one that contemplates every aspect associated with the process, including potential complications.
The rights of surrogates depend also on the law governing surrogacy in the state where the arrangement is done. We recommend that you discuss this issue with your attorney who specializes in reproductive law in your state.
Suggested for you: What Is a Surrogate Mother? – Everything You Should Know.