UPS for router

[Meddling-Monk]

Would plugging a multi plug adapter into one of the battery back up plugs work? Or is it just one item per socket?

You can use multi-plug adapters into one of the battery back up sockets. But as @5abr3 said though, you shouldn't overload a particular one socket this way.

However, given you're not trying to plug in a power hungry PC with a 4090 a 90" TV and a fridge at the same time with a hair dryer (which on pull would easily overload even the more expensive consumer UPS available) and only plugging in ancilliary devices, you should be OK.