Your main problem is likely to be discrimination.
We in the UK call these things Residual Current Devices(RCDs), they work particularly well for us because our entire system is neutral grounded using a 3 wire system.
The problem with multiple RCDs is that they not only will have a tripping current, they also have tripping times, so that a surge will not cause unwanted interrupts.
Ideally you put RCDs with longer trip times further toward the incoming supply connection, so that those further down the line trip first.
Your problem comes when you install units with ostensibly the same tripping time, because the reality is that there will always be some small differance.
This can then lead to unwanted upstream tripping, and leave the downstream device still on and can then lead to problems working out which is the faulty circuit.
This is where you pay for a person who knows what to look for in manufacturers specifications instead of doing the job yourself.
This can happen with fuses as well, but fuses tend not to be used in the same way so the safety issues are differant.