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

This depends on the position of the implants as well as force factors, length and width of implants used and cantilever. Sometimes only 10-12 are placed on the lower.

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 

The location of the back implants have a major role for how far the teeth can be spread in order to have 24 or 28 tooth. 24 teeth should give very good chewing abilities without risking adding more teeth in the back that might affect the strength of the denture and the implants by cantilever effect. 

Trust me you will look good and eat well with 24 teeth. You don't need all the teeth till the third molars to eat well. 90 percent of our chewing is till the first molars and the second and the third molars play a minor role in chewing.  So please don't worry about not having all the 32 teeth back. 

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.