So, the number of justices on the Supreme Court has been a matter of law since 1869. Did not know that.
Then how did FDR’s court-packing attempt come within a whisker of being passed by Congress? Would it have been ruled unconstitutional if it had? It would seem so.
I'm no constitutional scholar (Obama took my law school slot, but that's another story). But I'm guessing a president could legally pack the Supreme Court if he had the votes in Congress.
If the Wikipedia article is correct, all you'd need do is get Congress to authorize a Supreme Court of, say, 20 Justices. Then you could just appoint 11 more Justices.