if when these cameras turn off and on, its new clips might have to do extra steps. i never tried this, but can give it a shot.
Adobe Premiere Pro Help | Multi-camera editing workflow
Select the Create Single Multicam Source Sequence option to combine the clips into a single multi-camera sequence. Select this option when the coverage from the individual shots has gaps, and you want to create a sequence that preserves the gaps. If you do not select this option, only overlapping clips are combined and clips with no overlaps are left unused.
so what i think might work, is to select all the clips from one camera, choose create multicam sequence, then check the option for "Create Single Multicam Source Sequence". do this for each camera, could also name each one by camera to keep the multicam sequences organized in your bin. then it gets tricky, select all of the multicam sequences and create another multicam sequence. if it wont let you sync by timecode, you will have to use another method such as making a marker on a frame at the exact time on each multicam sequence. then drag this new multicam sequence (which holds each camera's multicam sequence) to the new item icon to create a timeline sequence. then you should be ready to multicam edit. since this is nested a few times over, you might want to pull out and use an audio track to the main timeline edit sequence instead of having it use one in the multicam nested sequence.
if you need to edit the clips inside a multicam sequence you have to right click it in the bin, and choose edit in timeline. double-click doesn't work. this will let you manually modify the layout of that sequence to fix something.
