My carrier infinity gas furnace goes on and off mmany times before it reaches the set temp. It has a two stage blower motor. The unit is only three years old. Board and thermostat have been replaced.More intake ducts added. None of this helps

If you have the infinity control(Thermostat). It tells you what is going on all the time and what faults you have had from day one of installation of the system. It keeps track of low and high fire times of the furnace. If you have this control and they can not figure it out, they are not looking at the service side of the control.