Basically for a race with multiple open seats, just keep repeating the "compare the top two rated candidates" step filling each seat with the winner of the comparison until all seats are filled, doesn't just fill seats though, because the win matrix can also be used as a list of succession in case of recalls or deaths or resignations that'd leave a vacancy.

We'd see a lot of districts seat all dems and reps at the outset, but over time you'd see a much more diverse cast and a much less party hierarchy controllable process.