In class I presented three basic forms of koshinage from shomenuchi ikkyo.
To start, assume the kihon response for ikkyo, but because uke was not controlled through the arm alone, uke starts to stand. Nage therefore responds by closing the gap (entering) while using the hand once on uke’s elbow to take uke’s hip, load and then throw koshinage by stepping back.
Tissier sensei presents this basic form as the first presentation (albeit starting from ai-hanmi katate dori not shomen):
Tissier sensei’s video presents numerous additional possible variants.
In class, we covered only three – the basic, then the reverse of the basic (which flows with uke as they stand so nage radically turns in and throws off the opposite hip), and then the Kanai sensei projected koshinage. I cannot find a video of Kanai sensei demonstrating what I clearly remember seeing, but Yamada sensei does a version of a forward projection from kata menuchi:
Ikeda sensei produced an interesting compilation video on koshinage that is worth watching for its history, application against weapons, and training methodology: