It will work just keep in mind your bigger tank is only going to start affecting the 13ci whenever it drops below your other tanks output pressure, and is only going to add air to it at that pressure. So if your bigger tanks reg output is say 550psi or something, your 13ci won't feed from it until it drops below that pressure, and at that point it'll only be constantly fed air at 550psi.
So it depends on what pressure your gun runs at, how big your other tank is, if you go full-auto, and what output pressure that tanks reg is at. The lower the guns operating pressure is than your second tanks reg output pressure, the better off you are. If you go solely semi-auto you should also be safe.
Long story short, it should work fine.
Just run the 13ci in the stock as normal, and get the biggest carbon fiber 4500psi SHP tank you possibly can (90ci and up) and hook it up to it's fill nipple when it runs low or leave it on the whole time. Just remember even after the 13ci would run out, and you run it through the fill-nipple, and then that runs out, you can connect the bigger tank to a gun and still have air left. It's not an efficient set-up but It should work.