Mamiya TLR left hand 'flash grip'

...is it possible to attach a quick-plate to the underside of the plate? This is not possible with the grip I already have - it's the one with the built in trigger.

The multi-angle version has a tripod connection thread, so yes for that one.
For the older, simpler one, I have an old one that was modified to add a tripod connection thread to the to the camera attaching bolt, so I can do it with that.
If I were to do the modification today, I would have that bolt taken out and try to replace it and the attachment bolt in the quick plate with one, longer bolt - leaving the quick plate essentially permanently attached to the grip.

There are numerous left handed grips that will work with the Mamiya TLR. Just start searching and choose the one you want.

The Mamiya left hand trigger grips do, of course, include a very good mechanical trigger that mates directly with one of the two shutter releases on the various versions of the RB67s and C330 bodiess, as well as the special anti-twist locatng pins that mate with the matched holes on those cameras.