I’ve got a Multisite network that looks something like this:

Site A
Site B
Site C
Site D
Site E

and have a set of Categories like this:

Category A
Category B
Category C
Category D
Category E

These Categories relate to the Sites. i.e. Category A is what Site A is all about. However there will be posts that may be relevant to multiple sites in which case you would select multiple Categories.

So, each Site would list all Categories (as check boxes).

Is there a simple way to implement this type of functionality (either via a plugin or some simple WordPress code)?