There are several tricks – appointment of biased judges and court packing – to affect Supreme Court decisions. There is one democratic method method – amend the constitution as authorized by its terms. Right wing unhappiness with the Supreme Court goes back to the school desegregation decision of 1954, and continued with the decisions upholding rights of criminals, prohibiting the death penalty, recognizing a right to birth control, and rights against gender discrimination.
If Roe v. Wade is overturned, I would hope that supporters of abortion rights seek to amend the constitution. It takes a long time, takes super-majorities, and lots of money to drive the campaign for the amendment, but I think it could be done. Messing with the court itself, using political tricks, hurts the court and hurts democracy.