I know many people following the modular route who have been through 4-5 schools.
1) PPL
2) Hrs building - sometimes multiple school (I did mine at 3)
3) ATPLs
4) CPL, ME, IR
5) MCC/JOC
Some airlines have an issue with you doing hours building abroad (I was personally asked that very question in two interviews), but different schools should'nt be too much of an issue. That said, with so many students going through the integrated factories, going through multiple schools can sometimes look a bit messy.