Not sure if this is exactly what you'd wanted (ie. insect screen 'door' as 3rd leaf?) but I made these various triple pocket sliders in about 2 minutes using Cadimage Doors + Windows.
I've been using Cadimage Doors + Windows api for years now, and they are by far the best door & window solution for ArchiCAD.
Can't recommend them enough, and very affordable (about US$470 for a single-user licence). I'm not a rep for Cadimage - just giving credit where it's due.
Many previous employers have (predictably) asked:
1. "why isn't their code implemented as standard in ArchiCAD?"
2. "why should I buy another door / window tool when ArchiCAD already has one?"
Simple answers:
1. ArchiCAD supports 3rd party add-ons, allowing others to build on the solid base that is ArchiCAD (and there's copyright issues of course)
2. these guys do it WAY better
ArchiCAD 24 (build 5004)
MacBook Pro (16-inch, 2021) Apple M1 Pro 32GB RAM | MacOS 12.0.1
Melbourne, Australia