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Officially it stops at 20. Many GMs would probably expand that for you, though.
LOL, I totally knew this was coming up soon with all the Aasmir oracle FC talk!
If your playing in PFS, your currently capped at 20, otherwise talk with your GM.
I have one of these guys in a campaign and the GM is going to let my companion pick up class levels for every 2 effective levels earned. That seems pretty reasonable to me and easy for a gm, but I bet if you put the progression in excel and dragged it down it would auto figure animal progression out for you pretty easily.
Everything in the chart is linear progression. Everything except Link, Share Spells, Evasion, Devotion, Multiattack and Improved Evasion.
Things with linear progression can extend beyond the listed values.
Thus HD, BaB, Saves, Feats, skills, tricks, natural armor improvement, and str/dex improvement all continue past 20.
Nothing suggest that you can progress the animal companion beyond was is written. The class ability caps a lvl 20, so that is the max, as far as RAW goes.
Since the chart has a linear progression, it is quite easy to do so as a house rule. As a house rule however, it is entirely up to the gm and gaming group, to consider the balance and flavor implications of doing so.
There is some snippet in the book about this, in the game mastering section. I'll try to look it up later when I have my book.
Officially on what basis?
How weapon damage die increases with size modifiers and effective size modifiers (stuff like lead blades) is also a case of the official data being limited to a table one can easily exceed, but I don't think anyone believes weapon damage is capped by that.
On the basis that there are no official rules to go past it. Anything that moves the animal into level 21 is a houserule. I am not saying houesrules are bad, but it won't be official.
Since this would be a home game anyway the GM can just try to make educated guess on what an expanded table would look like for an animal companion.