I've mixed feelings about MMPR, mainly because it's subject to collusion via decoy lists, party splitting and the like, so it ends up devolving into parallel voting, which is susceptible to gerrymandering of constituencies. It works well in a lot of places (Germany, Scotland, NZ, &c.), but not so well in others (Venezuela, Hungary, &c.).

How would adding approval voting into the mix improve MMPR as you see it? It's an interesting idea for sure, especially as approval voting eliminates the spoiler factor in single seat elections you get in FPTP, and it's simpler than IRV.