Are the requirements for the Multi Engine Instrument Rating the same as Instrument Rating in Canada or is there a separate exam for each of them?
Your IFR is either Group 1, 2 or 3.
For group 1 you have to do the ride in a conventional twin, which means you need a multi-engine rating first. There is no written exam for the multi. It's just the training course and recommendation from the instructor for the check ride.
You can do a Group 3 IFR in a 172, but for the Group 1 you will still have to do a new check ride in a twin, so there is not much point in doing a Group 3 unless it's just to fly your own airplane IFR.
Just about everybody incorporates their multi engine training into the IFR training, does the Multi checkride at some interim point, then the IFR checkride in the same twin later on.
The main difference between the IFR checkride done in a single, vs one done in a twin, is the examiner gives you an engine failure drill to do on a missed approach when you do it in a twin. Otherwise they are about the same.