There is peril in having too many intermediate appellate courts in the vertical structure. The first is the absence of finality - litigation drags on for longer. The second is defining the function of the new intermediate courts. Generally, it is a good idea to have one trial, one appeal that is a (relatively) wide ranging review of the merits, and one ultimate appeal for the odd case that throws up something deep, or to resolve differences among appeal courts, etc. You also need an ultimate court of appeal for disputes between the states. Of course there is no reason why the number of appellate courts in the horizontal axis can’t be increased - there is no magic in the number 9 as the number of Circuit Courts. There could just as easily be 12.
In America, of course, the position is complicated by the presence of various constitutional arrangements which increases the number of potential appeals, but at least the role of the various intermediate courts - what issues they can look at - is fairly clearly defined.
Just injecting another level of appeals, without indicating what it does that value-adds to the process below it or above it, doesn’t really help things.
Having two simultaneous Supreme Courts cannot work. As pointed out above, there will necessarily, and quickly, be differences just as there are among the Circuit Courts. One court of ultimate appeal is a hallmark of national unity. If you have two, then one part of the country is living under different rules than the other, whether the jurisdiction is divided geographically or in some other way. Why not have two presidents on the same principle? Very quickly you wind up like the Eastern and Western Roman Empires.
The Supreme Court has a mechanism for controlling its workload, as do all ultimate courts of appeal. It doesn’t have to take all the cases that people want it to hear. It can decide that the point raised is of insufficient importance to warrant Supreme Court review, or use a variety of other devices to refuse a full hearing. It knows how many cases it can effectively handle a year. It applies triage. There are some 10,000 applications a year to the Supreme Court. It hears about 100.
Having said that there needs to be a single ultimate court of appeal, there are countries with an ultimate court for general issues and a purely consitutional ultimate court. This seems to work with goodwill, but it is always possible for such courts to disagree with each other about where the boundary is, to much confusion. On balance, the single court model is (IMV) preferable.
There is something to be said for appointing more justices, or for sitting benches of less than 9 in given cases. Many other parts of the world sit less than the full bench in most cases. Of course, I suspect that some judges fear that the results would be stacked if they didn’t sit, but that is a matter of judicial culture. It doesn’t seem to bother other countries. The convention is that even if (say) 5 judges are listed from those available for a particular appeal, anyone can “pull up their chair” and join in if it is a matter of particular concern to them.
And there is much to be said for a mandatory retirement age - 70 or 75 perhaps. For every legal luminary you sadly lose by that process, you happily lose many more duds who are past it. The age limit preserves the independence of the judiciary yet substantially (but not completely) removes the arbitrariness of juges being able to manipulate which stripe of government will appoint his/her successor by a judicious choice of when to resign.