

Following the pattern of bisected, which is Latin, 4 through 6 would be quatresected, quinquesected (or cinquesected), and sexected. If you prefer to switch to Greek roots, it’s tetrasected, pentasected, and heptasected; 2 with a Greek root would be disected, but that already means something else.
Comparison to quartered is uglier; 2 is obviously halved, but 3, 5, and 6 are harder. My first instinct was ‘thirded’, but I don’t think so. ‘halved’ ≠ ‘seconded’, and I can’t think of anything that would be to ‘thirded’ as ‘halved’ is to ‘seconded’
Conveniently, if any states were to join Canada, they would most likely do so as territories (at least initially), and so would be somewhat politically neutered.