Can you change the motor on this gearbox?

My question is that is it possible to change the motors on a gearbox like this( and try to fit a slightly larger one like this( By the way, the reason im planning to change the motor is because my motor shield(Adafruit) needs a motor thats 4.5-25v and the one that comes with the gearbox isnt enough. 

4.5 - 25V looks OK to run a 12V or 6V motor to me.

Do you really mean you want more TORQUE than the little motor can provide ?

I don't see why you couldn't do it, though you may struggle, if the shaft on the motors is of a different diameter.