(Posting a self-answer with my results so far, since nobody has answered yet).
Firstly there's no simple way to turn a single-boot NOOBS into a dual boot. You had to have selected the dualboot when first installing. I decided to save my data, wipe the SD card, and download berryboot which allows you to add new OSs at any time, and then reinstall Raspbian via berryboot.
Secondly: on the Raspberry Pi, the firmware is a part of the boot loader (It's not flashed into BIOS like on a PC). RasPlex is a complete solution; RasPlex and Berryboot each have their own firmware module.
It turns out that the RasPlex development team often make their own firmware improvements, to fix playback glitches. So for the best experience you have to use RasPlex in a single-boot scenario, i.e. if you want two boot types then get two SD cards and manually swap out. The posts on the RasPlex official forum all assume that you won't be dual-booting.
Nevertheless I did manage to set up dualboot of Raspbian and RasPlex and have not had any issues so far. It wasn't straightforward - I had to mount the RasPlex image and run some preprocessing on the contents to produce a file that is the right format to be accepted as a BerryBoot boot image. I found those instructions by googling. I'll write another Q/A here on that soon.