How many quirks can one have?
The manga has an answer to this question - and it was mentioned already in the anime:


   The quirk All for One allows its holder to steal as many quirks as they want, as well as forcibly give those quirks to others (this is how the Nomus have been created).





   No limit has ever been mentioned, though having many quirks given to most people will cause a mental breakdown (explaining why Nomus act as mindless beasts).