The term 'current' does not exist in EASAspeak - a rating or certificate is either valid or it isn't. If a rating is not valid then you do not 'hold' it and EASA requires that it is removed from the licence within 5 years. In the case of the UK, when ratings are removed they are recorded under 'Ratings Previouly Held' (which is not part of the licence). However, this is not an EASA requirement and may not be the case in other member states.
An applicant for a first MPA type rating course is required to hold a multi-engine IR(A) (FCL.720(d)(2)).
An applicant for the issue of a second or subsequent MPA type rating shall hold a multi-engine IR(A) (FCL.720(f)).
For a second or subsequent MPA type rating, therefore, you do not need to hold an MEIR to start the course but you do need to hold one when you apply for the rating. The IR will be revalidated/renewed on the specific MPA type during the course/skill test.