Only the lender can insist upon a second appraisal, and typically only you as the buyer can make a request for another, which might or might not be honored. You can offer to split the cost of the second appraisal if you're the seller.

Is it worth getting a second appraisal?

When considering second appraisals for mortgage transactions, there are generally only four acceptable reasons why you can get a second appraisal: There is a reasonable basis to believe the original appraisal is flawed or tainted. The original appraisal is dated/too old. ... A second appraisal is required by law.

When can a second appraisal be ordered?

Page 128 states: “A second appraisal may only be ordered if the Direct Endorsement (DE) underwriter (underwriter) determines the first appraisal is materially deficient and the Appraiser is unable or uncooperative in resolving the deficiency.