The problem is that you need to modify many parts to support 4 motors in parallel instead of 3. So all arrays need extra space for 4th motor and you need to adjust the math routine to a 4th axis. Not that difficult but changes at many places so resulting firmware is incompatible to existing version making updating a bit harder as you always need to check if one of your mods gets altered.
Also I would advice using a due based board since you need more speed and ram.
Regarding stability, you will get one problem as the model becomes statically undefined. As shown in the image it works with 3 of 4 arms perfectly. This means the 4th position is exactly defined und must at all times be where it should be or you will loose steps or platform will start to rotate. Since moves are all nonlinear each computed move must be small to reduce the error to something that is smaller then play room. With due you should be able to do 500 updates per seconds, so it should suffice. But you should be aware of this constrain.
