Why not increase it to 12-11 in the Democrats favour if they are increasing it?
Why would you break convention to increase it, yet still fall short of a Republican majority
I think the big problem becomes in opening Pandora's Box (although with the GOP, pandora is usually the name of the dead hooker in the trunk and her box is...well...you get the idea)
It's all very well adding more SC justices to balance it out, especially after McConnell's absolute ratfucking of Obama's last pick and Trump's obvious deal with Kennedy to allow him another pick, but once you open the door to that convention, you can't close it again. Next time a GOP goon gets in, they can do the same to restore "natural justice" after Biden "artificially changed the make up of the court because it was conservative" or some such bullshit. Obama had to use lots of executive orders to do anything during his last term because of McConnell's zombie senate, bit that just meant Trump used even more to bypass oversight and felt it was fair to to do so by pointing at Obama's EOs, just leaving out the obvious context.
I'm not saying they don't have the moral or regal right to pack the court given the fuckery involved, but I think I'd concentrate more on closing every fucking loophole and good faith convention the GOP has used over the past decade. I'd absolutely put in law, not convention or anything, that Supreme Court picks last up until the end of term regardless of the Senate Majority. I'd strip some of the power from the senate and House majority leaders in being the sole arbitor of what comes up to vote. I'd place limits on time between bills going from house to senate (say 100 days) without being voted on. If the time limit passes, it's assumed that concensus is reached and the bill automatically becomes law. That sort of stuff isn't sexy, it isn't going to grab as many headlines as court balancing or what have you, but will be much more effective in the long run of restoring some balance of power between the various powers and make ratfuckery harder.
Edit: after reading JCs post below, I would absolutely put in law that the President is not immune to charges while in office. Dump that fucking DoJ memo Barr and Trump have hidden behind to the curb and clarify in black and white what the President can and can't be charged with whilst in office. At the very least, codify that the statute of limitations is paused while President if you can't get everyone to agree on actually having them accountable while in office.