It can supposedly be done.
The issue is whether there are any total show-stoppers in the design. The Phoon already has a moderate approach speed, so a carrier version does not need a completely different wing (see Dave C). How much bring-back you have at that point, I don't know (but it does not have to be much to beat the F-35B).
The Phoon allegedly has enough hot air coming out the back to dispense with a catapult, as the Russians do (and as the MiG-29 will do for India). This avoids structurally redesigning the entire nose gear and front end.
The Phoon does not have the over-the-nose view that the USN would want, but there's a lot you can do with cameras and synthetic vision these days.
Doable, but expensive... But if you get into a situation where Dave B won't do its thing without redesigning the engine, which A and C don't need, and the UK and Marines get faced with the bill...