Each engine varies. GE, our engine manufacturer recommends 2 minutes (CF 34). Rolls Royce recommends between 2 and 4 minutes, depending on oil temperature.
Towing aircraft is a good idea and it has been used from time to time, assuming a long distance tow is approved at takeoff weight with passengers onboard. But you start to incur other costs and complexities. Who is in charge? How many ground crew? Some believe you have to have wing-walkers whenever you have a tug attached. Wing-walkers will reduce your towing speed. How many more tugs will be required? How does the tug get back to the apron? What processes will be in place for emergencies? Figure that lot out and let us know.