This was exactly the scenario which raised the original question - had someone in a syndicate wanting to do CRI work but was studying for the full blown FI(R).
I can find nothing in the regs to say that you can't hold an FI(R) and CRI together - but then.....
You can hold both at the same time. I hold both an FI and CRI SE/CRI ME. My colleague holds an FI(R) and went and got a CRI SE/CRI ME specifically because he will never be in a position as a company pilot to get the restriction removed.