I'm going for a triple pickup in my next custom build - It's not at all crazy, but positioning is key. The third pickup should be getting something the other two don't.
The
1980s PRS Bass IV had three single-coils, two roughly where you'd put J pickups (but nudged closer to the bridge) and one right at the end of the fingerboard, similar to a Ric / Hofner etc, for that extra-bassy fundamental, which is why Robbie Shakespeare loved it for reggae/dub. All three pickups were at different positions and provided a variety of useful tones - sharp bridge, balanced middle, extra bassy. It used a 5-way rotary switch, but I think I would have gone with 3 mini toggles and independent volume controls myself.
By contrast, the Fender Urge, with it's J/P/J setup, clustered the pickups very closely together - I had one and I don't think the P pickup really added much (matter of opinion). The great thing about that bass was its compactness and the really nice neck shape, very playable.
The other option is something like a "strat bass," evenly spaced, possibly with one at an angle. Fender's short-lived Rascal short-scale had 3 lipstick pickups in that configuration.
In terms of pickups per se, it really depends how precise you want the area of string to be detected to be. Going with a narrower coil like a J will detect a smaller area, letting you zero in on specific overtones with more of a scooped midrange, whereas a P creates a bit of natural phasing due to the split coil, with more mids and lows.
An alternate configuration might simply be a dual-coil humbucking soapbar plus a single coil, with the ability to split the soapbar or to do series/parallel switching.
