Ok. So there is not the toggle switch I was talking about.
Moreover, BKP sells a "CRL 4-way Tele", but I did not found anything about it. (I am actually not an expert in toggle switches.) However, I found only one type of 4-way toggle switches. So I assume this is this type: Oak Grigsby 4-Way Lever Switch. (There are 2 poles/switches. Each one have 5 connectors: a given connector is connected to one of the 4 others according to the toggle position.)
Anyway, I tried something I did not think about: inverting the wiring of one humbucker when used alone (what has thus no effect on the tone).
What you can do is:
1) Still controling coils with pp pots (series, coil splitting and parallel):
- No push/pull activated => standard wiring: coils in series
- One push/pull activated => Single coil
- The other one activated => The other single coil
- Both push/pull activated => Coils in parallel
2) Having, according to the 4-way toggle position:
- Neck only
- Neck + Bridge in parallel
- Neck + Bridge in phase inversion and in series
- Bridge only
However, when inverting phase, I cannot change the coils combinations to keep cancelling hum.
I am not sure what phase inverted pickups in series does, but it might be interesting: trebbles shall still be boosted, and using series keep or even increases the output power (usually lowered when inverting phase while keeping pickups in parallel).
I think that what I propose here can be really nice... But is having "phase inversion + series" better than having just "PUs in series"? I do not know. Personally, I would try both.
Now, it also depends on your needs. If you play many brutal rythms, and want to increases your guitar output for more distortion, series might be better. If you want an ultra-bright tone, you might prefere phase inversion.
PS: I checked, using the 5-way toggle available from BKP will not allow you to get "PUs in parallel" + "PUs in series" + "phase inverted PUs".
PPS: I think we saw every interesting possibilities (using material from BKP website):
- Push/Pull pots: coils in series / single coils (2 combinations available) / coils in parellel
Toggle: Neck alone / PUs in parallel / PUs in series / Bridge alone - Push/Pull pots: coils in series / single coils (1 conbination available) / phase inversion between PUs
Toggle: Neck alone / PUs in parallel / PUs in series / Bridge alone - Push/Pull pots: coils in series / single coils (2 combinations available) / coils in parellel
Toggle: Neck alone / PUs in parallel / PUs phase inverted and in series / Bridge alone
PPPS: If later you want more, you can still buy a super switch to get (1) and (3)... But I think you will have far enough with one of those three wirings.