An MEIR is required to commence a FIRST multi pilot type rating.
An MEP is required to get an MEIR.
Until about 5 years ago you could get an MEIR without holding an MEP rating but that loophole has been closed.
The airlines don't care about an MEP rating. Its nothing to do with base training either - why would a piston rating allow you to fly a jet? Base training is done after you have passed the type rating check for the aircraft.