With the all on four implants will I be able to have more than 24 teeth?

yes you can , as long as you have great support, also you will need to have good analysis of phonetics,due to different factors that might interfere. 

Extending teeth beyond first molars is determined by where the posterior implants are going to be placed. Typically, All on 4 patients have poor bone availability in the molar areas, so implants have to be intentionally placed at mechanical inclinations. What your dentist is most likely trying to avoid is a long cantilever which can overload either the implants themselves, or the prosthesis leading to fracture and ultimate failure. 

Hi and thank you for your question. Typically the All on Four procedure will extend a prosthesis to the area of the first molar, this means 12 upper teeth and 12 lower teeth. It could be possible to extend the prosthesis if the is more implant support in the back, this could be accomplished with sinus grafting.
Good luck to you, 
Dr. Juan C. Arroyo
Oral and Maxillofacial Surgeon