Lyle Denniston, the 95-year-old former SCOTUSBlog reporter, conveniently lists possible Supreme Court reforms. They are not comprehensive.
(He frames it as "changing" the Court.)
For instance, they can reform qualified immunity or address national injunctions. If you wish to count them as court reforms. But he does generally cover the gambit.
The No King's Act or an amendment doing that also can be tossed in. Ditto something about abortion or some other major "mistake" of the current Supreme Court. These are basically Court reforms.
We can expand the Court and/or (the first shouldn't foreclose the second) have term limits. Term limits, realistically, require a constitutional amendment. They probably do constitutionally. Also, realistically, it will be hard to pass legislatively since many moderates will think so.
I have talked about expansion. I respect the demand, though I'm wary about it. I doubt it will happen. If it does happen, we should also have the ability to do many other things.
Term limits should have broad support. Enough?
Well, push other reforms; maybe there will be more support for it to be a compromise. It's time for some amendments.
Take away some of the Court’s power to decide specific categories of cases. The Constitution says that Congress has some power to impose such limits, but how much may depend upon whether the Court would strike down any such measure as an unconstitutional interference with its independence, which the Court vigorously defends.
They can also require the Supreme Court to take more cases. That might not be ideal, though some people do want them to do that. Another approach is to channel certain cases to a particular circuit (D.C. leans liberal) or reduce the power of single judges somehow.
He also notes Congress can require a supermajority before a law can be declared unconstitutional. I'm not honestly sure about the constitutionality of that approach. Ohio used to have that (see the opinion below in Mapp v. Ohio).
The Court can be required to explain itself in the shadow docket. That can include providing the votes on certain orders or other actions. I think that might be gamed somehow, such as having one go around and the final on the record vote will largely be unanimous.
The last three are the most likely. They can "fast track" responses to Court rulings. They can (and very well should) have binding ethics legislation. And they can (the current chair of the Senate Judiciary Committee supports this) require video.
If the Democrats do win control of one or both houses, they should significantly focus on the Supreme Court, including investigations and fact-finding. That includes hearings about specific cases and issues.
Prof. Melissa Murray, a co-host of the Strict Scrutiny Podcast, took part in a pre-Dobbs hearing about abortion access. This is the sort of thing we need.
Some people are PASSIONATE that we need court expansion. Well, I doubt it will happen. But okay.
But there is other stuff to do.