Upgrade BLDC motor controller (ESC) to higher wattage (replace mosfets/shunt)
I was wondering if I could upgrade my current bldc motor controller (three phase motor) to a higher wattage/output power by doing the following modifications:


Probably - but it depends to some extent on the application and how sophisticated the controller is. I could attempt a point by point response but essentially they are broadly covered below for 3X increase in power, and at 10X VESC is almost certainly an attractive choice. 

You mention "a current shunt" suggesting that gross motor current rather than phase currents is being sensed, which in turn suggests that the controller is 'not too magic', which is good in this case. 

If the controller is NOT using FOC control and trying to implement deep magic, as modern advanced controllers do, thn more and bigger of the same may well be good enough. If the controller used advanced methods to implement vector control and if the motor + controller were designed to work together then some of the magic may need recasting to make things work as well.

A FOC controller will usually use current sensors in at least 2 phases (the theory being that the third phase can be inferred) and the latest VESC iteration uses sensors in all 3 phases as Benjamin Vetter has concluded that the difference between theory and practice is greater in practice than in theory.

All that said, if you are going from 1+ kW to 3 - 5  kW load you would probably benefit from a FOC based control strategy. If you are willing to change MOSFETS, shunt, heatsinks and more then implementing an open source VESC ESC may do you major favours.

My recent SE EE answer here provides links to various VESC related sources. 

There is another open source ESC that was popular a few years before VESC gained popularity. It uses a processor costing about $1 in 1's whereas the VESC MPU is "somewhat more". I'm 'out of country' at present but can look up details in a week or so if of interest.