Here is my suggestion. I haven't worked out component values, but the idea is that you still use the rheostat current to run the motor, but add to that current in a fixed ratio to allow for the larger motor.
R1 and R2 are low-value current sensing resistors, and their ratio will be the ratio of rheostat current to added current. For instance, if you need three times the current, so you need to add twice as much current as the rheostat delivers, you could have R1 at 0.2 Ω and R2 at 0.1 Ω.
Design considerations:-
The Op-Amp needs to be a rail-to-rail op amp.
The MOSFET is a P-type and needs to take all the additional current, and will generate a lot of heat.
The resistor and the capacitor connected to the inverting input are to reduce high-frequency gain and stop oscillation. 10 kΩ and 1 μF would be a good start.
R1 and R2 need to take the rheostat current and the additional current respectively, so they need to be suitable power resistors.