Here is mine to kick it off:
They're there to show their wordplay is too much fun for only two to four people, so come to the fore and join in the play by making a play or go buy a room at an inn.
they're, there, their (+3); too, to, two (+3); for, four, fore (+3); play, play (+2); by, buy (+2); in, inn(+2).
Preliminary answer. The work to get a definitive answer is more than I have time for.
As OP points out:
Also, as OP pointed out:
As with all such problems, the goal is to try to have each test divide the remaining set of possibilities into 3 groups, as evenly as possible.
The only possible option for the first test is to weigh N coins on the left versus ...