Hopefully this will make some sense. I am not sure if EASA has changed how things work with this.
You can not do your MEIR test until you have a MEP rating. You cannot combine these tests.
You can however combine the CPL and MEP tests, and (in the UK at least (I think)) can combine the course to do MEP+CPL as a 28 hour course and then a 45 (inc. -10) hour MEIR course.
If you want to do the IR first, you would have to first do a 6 hour MEP course, then the 55 hour MEIR course, followed by a 15 (inc. -10) hour CPL course.
People will say that the MEIR is the most difficult course and should be left last but some people find the CPL more difficult.
I personally did it in the order: SE(IR) (45h) > CPL/MEP (9h SEP, 6h MEP) > MEIR (5h). This worked out the cheapest for me but required quite a lot of effort studying procedures, checklists and the POH outside of the flying time to get myself confident for the MEIR test with that many hours.
Another thing I would add is; if you are aiming for the airlines (I presume you are given you mentioned an MCC), it is wise to do CPL and IR at the same school.