In several, including the Strathspey, The Shepherd's Crook (MacNab), The set consists of a threesome, a single Partner group of 3 Dancers only, usually a Man and 2 Ladies. There is no Progression.
In some others, including Nifty Ninety, The set has 3 threesomes, not gender specific in this example. The Progression options are as for the 3 couple set.
Another group is usually defined as being made up of pairs of Longwise sets, side-by-side. Logically, The set should be regarded as having foursomes (pairs of Couples) as the Partner groups but some of the many options for the Progression do not leave the same Couples side-by-side when each Repeat Finishes and so the complication of The set being Progressive by Partner would have to be invoked. Amazing Grace is an example for 8 Couples (4 foursomes); Just A Dozen is an example for 6 Couples (3 foursomes).
There are a few dances for 7 or 8 individual Dancers, of which The Eight Of Diamonds is an example, in which 6 Dancers are disposed on the Side lines of The set with the additional Dancer(s) on the Centre line. The Progression allows every Dancer to perform once in every Place.
The set format for Lack O' Men is described by the deviser as Longwise, Starting with Ladies in the Corner positions of a 3 couple set and Men in both 2nd places. Arguably, however, it should be regarded as a Square set for 2 threesomes (each Man between two Ladies).
The Willow Tree has the Longwise set format for 8 Couples; it is logically similar to many dances in a 6 couple set in that the Bottom Couples perform a mirror image of that by the Top Couples.
Riverside is a Ceilidh dance in a Longwise set for 3 or more foursomes.
Kandahar Reel is a dance for 4 Couples in the Active set, normally Repeated by 1st couple from 2nd place of the Full set; the devisers originally specified 6 Couples for the Full set but the RSCDS published a version with 5 Couples. It can easily be adapted for a Full set with only 4 Couples with 1st couple Dropping to 4th place after the first Repeat.
Jimp Waist is a dance for 3 Couples in the Active set; the complexity of the Progression process requires a Full set of 5 Couples rather than the normal 4 Couples. However, there is so much difference in the instructions between the even-numbered and odd-numbered 32 bar Repeats that the dance is far better classified as a 5 Couple repeat in 5 couple set requiring 64 bars.