You can’t exactly run two OSes - at least not right now - but you can easily perform a full system backup with TWRP, install the other OS, do what you need to do there, make a full backup of that OS and switch back using the first backup.
PS: I believe the backup also saves the OS, but I haven’t yet actually tried restoring a TWRP backup from a different OS (version) than the one I was running at that moment. Maybe someone else can confirm?
PPS: I just remembered that FP OS comes without TWRP so I guess you’d have to port TWRP yourself. On the other hand you’d not need a full backup of FP OS if you only need it to download apps from the play store.
You could however - instead of using FP OS - use FP open OS with opengapps as one of your backup images.