How to control motors with higher power requrments than 35V 3A 50W

The Arduino is just the controller which drives the motor.

If you need more power at the outputs of the Arduino - and this is how each controller works - you need "power boosters". In the old days this was realized with relays, then with bipolar transistors, sometimes cascaded (darlington principle), today in most of the times with very powerful MOSFets.

So:

Is it possible, Or am I asking too much from the Arduino

the answer is simply YES.