When a bass has multiple coils, they can either be wired in series or parallel.
A stock Jazz bass with two single coil pickups are wired in parallel to each other. A stock P bass has two single coils which are placed side by side and are wired in series. If you have a bass with a single, dual-coil pickup (such as a Music Man), that one pickup can have a switch to flick between series and parallel wiring between the two internal coils. You can also add a switch on a P Bass to wire the split pickup in parallel, or add one on a Jazz to have the two single coils in series.
Dual-coil pickups can only be wired in series or parallel within the same pickup housing (some can do single coil, but the signal only goes through one of the coils - the second coil is bypassed).
Most soap bar dual-coil pickups and humcancelling inline split-coil jazz pickups are designed to be wired in series, but can be wired in parallel as well. Most MM pickups are wired in parallel, but series is an option.
When the pickups are wired in parallel, there is a mid scoop which takes out some of the overlapping frequencies. There is also a resonant peak in the higher frequencies.
When the pickups are wired in series, the overlapping frequencies are actually boosted as well as the lows, while the highs are muted... Pickup location plays a part in a P Bass's tone, but having that split pickup in series is a larger factor. The is mainly why a Jazz's single coil neck pickup doesn't sound the same as a P Bass.
Now things get crazy... Imagine you have a two pickup jazz bass and install two humcancelling inline split-coil jazz pickups. There are now 4 coils (two coils per pickup). You can wire two switches so that each pickup is either series or parallel (front pickup series/rear pickup parallel; both series; both parallel; and front pickup parallel/rear pickup series), then you can also have a third series/parallel switch to change whether the two front coils (series or parallel) and the two rear coils (series or parallel) are wired series or parallel between them (for instance, each pickup can be wired for series, but you can wire the pairs together in parallel, or series).
Yes, simplest way is separate V/V/V's or switches.
Blend pots can only blend two pickups at a time. You could only allow for two pickups at a time, run the pickups to a switch that decides which two are active, and then run them to the Blend. You could also have a V pot just for the neck pickup, with a Blend to blend between the mid and bridge pickup...However, you would need a separate volume knob if you want the mid/bridge blend to be quieter than the neck pickup.
The way Spock's Beard's bassist does it (with his 4 pickup Rick/Jazz bass) is that he just has a VVT setup with a switch that decides which two pickups (Rick or Jazz) are active. He does not have the ability to just have the two neck pickups on at once for instance, but 4 V pots would certainly allow it.
These multi-pickup basses with a bunch of options are tempting, but you can very quickly come up with a configuration of 5 knobs and 5 switches on a passive bass. This may be great for some people, or a distraction for others... For me, I would setup a test bench with a bunch of knobs and switches and wire the pickups straight to the bench, determine which different options offer the greatest benefits/variety for me and get rid of the extra stuff I'd rarely use (or wouldn't want to get lost in).
