https://www.businessinsider.com/how-gov-noem-trumps-desire-carved-into-mt-rushmore-2020-8
“The White House reportedly asked South Dakota's governor how to add another president to Mount Rushmore, and she later gave Trump a 4-foot replica with his face on it”
This is a lie: “It's not possible to add another president to the monument”
Above and all around the mountain provide multiple additional surfaces (some require significant rock removal, as did the existing surface) for sets of additional presidents, their daughters or everyone’s favorite general.