Many stages in Touhou spawn additional enemies depending on how quickly you defeat the midboss, to keep the stage from going below a specific length (and keep it synced to the music). Also called "bonus" enemies, though it's debatable whether some are a bonus (such as the infamous SA stage 5 popcorn fairies). Sometimes they're useful for scoring, while other times it's more profitable to graze or otherwise farm the midboss. I'm curious how common they are.
Note that some fixed-length stages will last longer if you take an especially long time on the midboss (such as by stalling out both a nonspell and a spell for graze), even if it has post-midboss timed enemies. I'd guess this is to prevent skipping almost the entire second half, as can occur in EoSD stage 1 and 5 for example.
Not sure if I made any mistakes here. Also it's not a very polished list; maybe adding more detailed descriptions later. It's hard to describe enemies that are mostly all fairies.
SoEW - 1, 2?, 3?, 4 both midbosses
LLS - 1, 2, 3?, 4 both midbosses
MS - 1, 2, 3, 4, 5, Extra
EoSD
1 (extra enemies can be nice for reaching full power sooner in stage 2)
2 (mostly a waiting period with no enemies, I think?)
4?
5
PCB - 1, 2, 4
IN - none?
MoF
1 (notably some enemies spawn during the midboss on Easy/Normal if you wait long enough)
2 (fairies drop star items-- very important for scoring!)
4 (bullet walls-- Momiji or these, your choice)
SA-- all sets of post-midboss enemies drop some star items in this game, important for increasing PIV in the 1-death scoring routes
1
2 (aimed bullet ring fairies)
4, second Orin only since the first is timed
5 (the infamous popcorn fairies)
6 (5-way kunai birds, the only case of any enemies after the midboss in a Touhou stage 6)
UFO
1
2 (circle-bullet fairies spawn in varying number)
5 (large fairies drop extra UFOs and lots of items, encouraging bombing Nazrin)
GFW - none?
TD
1 (spirit trios on alternating top corners)
2 (3-4-5 waves)
3 (blue fairies from left-right of screen)
4 (fairies from the top and spirits in the lower corners)
5 (single/double large fairies alternating)
DDC - 1, 2, 3, 4, 5, Extra (one of the few instances where this occurs in Extra)
LoLK
1, both Seiran appearances?
2
3 (flowery rings)
4 (arrow fairies in top right, highly profitable for invincibility grazing)
