To me this is a similar topic to when there are clones/copies/"whatever you want to call it" around and doing stuff. While sharing knowledge/sensation/whatever or not. Are those also the MC or is there the one MC and then there are copies.
And I can see people coming up on both sides of the aisle on this one.
To me those are different entities if they exist at the same time. Therefore LH and Serenity MC are not the same entitiy to me as they exist at the same time in different universes (and could even meet as Rin demonstrated dimensional travel). While I'm playing Serenity I "am" that MC and if the LH MC would appear he would be a different entitiy (to me as the MC) and vice versa.
Maybe I am just too smooth brained for multiverse shenanigans.