One solution would be to make the Supreme Court bigger. Not via the sort of “court packing” championed by people who just want more votes for their side, but via a reshaping of the Court itself.
For most of its history the Court has had nine Justices, though that number has varied over the years. The Constitution doesn’t set a number, leaving it to Congress.
I propose increasing that number to 59. Nine Justices could be appointed by the president, as they are now. The additional 50 would come from the 50 states. Each state’s governor would nominate a member of the Court from his or her state, who would then be confirmed by the Senate as usual. (Although if you really wanted to go for a major change, the confirmation could be by the legislature of that state).
The increase in size would mean that changes due to death and retirement would be routine—no more bringing Washington to a halt every time a Justice retires. It would also remove some of the Court’s mystique. People might believe in nine philosopher-kings in a temple of justice, but no one would believe in 59 philosopher-kings. Fifty-nine sounds more like a legislature, and if the Court is going to do legislative-type things, as it clearly does, maybe that’s a good idea.