There is no section that contains the limitation that you describe. The rating of a sub panel has to be high enough for the calculated load, and it has to be high enough to be protected by the upstream breaker. You can have a 100 amp panel feed a second 100 amp panel, and have that feed a 225 amp panel, and have that feed another 225 amp panel, and have that feed a 400 amp panel. Not a great design choice, I admit, and probably a huge waste of money. But still code compliant. Panel ratings are not the issue here.
Bob's point, I believe, is that you have to calculate the load, both on the present panel, and on the panel you propose to install. That is why he sent you to article 220: that is where it tells you how to calculate the load. If the total calculated load on the present panel, after all modifications are done, is within its rating, then you are OK.