To be honest I've done this before. Currently my 'Bitsa' Jazz has a MM Humbucker next to the neck PUP that's switchable (currently on/off) that works in parallel with my normal J pickups. It'll do standard Jazz, P bass and MM tones really rather well, but I'm wondering about a mud-bucker next to the neck that's also switchable (on/off) with a preset trimpot inside the cavity, so I keep the look of a Jazz control plate. I've just done a mock-up using images from GAK's website and I reckon it might be a step too far.
[url="http://s1221.photobucket.com/user/paul_510/media/JazzBassMonster_zpsbcbdeebd.png.html"][/url]
Tonally I foresee it being unbeatable - rather like having an active 'bass boost' knob without the electronics. I could combine the Jazz bridge PUP and neck bucker for a really biting snap with a dubby low end, or any other combination. Might need a LPF on the output of the neck-bucker though...
Aesthetically it might look better with a white pickup cover on the neck-bucker, a bit like Billy Sheehan's old Attitude basses, but without the dual output.
Or am I just going a bit mental?