You can do a JAA PPL/IR on the CAA Class 2 medical but you also need the JAA Class 1 audiogram.
This catches out a lot of people especially slightly older types. Each ear is tested at four frequencies.
The only way around this is to invoke the JAA Demonstrated Ability option but that one is available on renewals only. I have the references.
The FAA IR or ATPL doesn't have this stupid requirement.