I'm not sure at which layer this functionality would have to exist, so I'm just tagging this for my own stack.
In my specific case, I'd really like to map the [Function Key]-J key combination to the down arrow, [Function Key]-K combination to the up arrow on my laptop -- in other words, pressing Fn-J would simulate the down arrow being pressed. I'm running Arch+Gnome3.
I guess xkeycaps can't do key-combos. I know you can do custom mappings to various actions in Gnome, but can't re-map keys in this way.