Allow all the groups of 2 or more to board first (before the singles). (Most of) the twos, fours, and fives will leave an aisle or window seat open. The singles will then fill in the holes and almost everyone will get a seat together.
For example, assume a plane with 138 seats (46 rows - I'm ignoring the missing exit row seat on purpose to make it easier). The breakdown of parties might be:
- singles: 40 (40 people)
- doubles: 25 (50 people)
- triples: 9 (27 people)
- quads: 4 (16 people)
- quints: 1 (5 people)
The triples and quint will take up 10 full rows. The doubles, quads (assuming they sit 2+2) and leftover quint will take up 2 of the seats in 34 rows (25 + 4*2 + 1). That leaves those 34 rows with one open seat, and 2 rows (46-10-34) that are completely empty. All of the singles except 2 will get an aisle or window, and no party is broken up. (And yes, I'm ignoring through pax, late boarders, bickering couples, single medical pre-boarders, and lots of other exceptions).
They could still sell EB and give priority, but only within the two groups. In other words, EB or A-list or BS would get you closer to the front of the "party" or "solo" groups, but solos couldn't advance into the party group.
I think WN might get a side benefit of a little faster boarding, too.
Of course, A-list typically singles (like me) would not like this too much....EB would go down to near zero for the party groups, but might actually go up for the solo travelers.