The maximum (active) Dinoz you can have is 18.
If you have the wood skill Leader U, then you can have 21 (active) Dinoz.
'But I see people with way more Dinoz!'
Yes, those Dinoz are Frozen. That means you cannot use them, until you defrost them again. The points will still count and U skills will still work when a Dinoz is frozen.
Where can you freeze Dinoz?
You can do that at the Deep Gorges after talking to the Propotheller.