Here in the PNW we can't grow Lima beans or many of the long season common beans apart from growing them in a greenhouse. But we can more or less reliably keep ourselves supplied with pole snaps all of August through the end of October. Earlier if we grow bush snaps or start Emerite in pots.

Perhaps it is my Appalachian ancestry, but I consider full beans - beans that are eaten when the seeds are mature - to be superior to ordinary green beans. So the goal is to have full beans available every day for as much of the season as possible. Here is what I did for snap bean succession this year. They were all planted about June 1. Emerite and Fortex were enjoyed until the Aunt Jean's kicked in.

Emerite
Fortex
Aunt Jean's (good until they are yellow and starting to dry)
Anellino Giallo (good until they start to dry)
Red Eye Greasy/Hazard Fall/Leslie Tenderpod
Tobacco Worm (good until they are yellow and starting to dry)
White Simpson Greasy (good until they are yellow and starting to dry)
North Carolina Speckled Long Greasy Cutshort (good until they are yellow and starting to dry) - Dick