Don't take my word for it, but as far as I'm aware it's the decision of the CAA, or authority of the state you're in.
If the ATPL theory has been complete I can't see why you would need to do them again.
There are many modular schools that take on students just for CPL/ME/IR who have already done their ATPLs elsewhere. However, once you've signed up to an integrated course, you can't just swap onto another one.
We had a few students at my school who swapped from Integrated to Modular. The decision had to go through the CAA to be approved. I assume the school itself must also be aware and would have a person responsible for dealing with such issues.