There would be even more when you consider pickups could be wired series or parallel.
1 could be wired in series to 2 and three which are wired in parallel to each other and then in series with 5
or 123 in series or 123 in parallel
See what I mean? There are a ton of combinations...more than 26.
Reasonable, the hardware we use to switch would really only allow the use of 10 of those possibilities to be wired to the switch (In the s1 circumstance)
If you had a 5 way rotary switch change the function of the 5 way selector (the rotarty would be like the s1, but with three more positions), you would effectively have 25 available sounds. but to wire this would be quite a headache without a circuit board.
In my oppinion.
I used to think I wanted all the selecting options. After years of trial I decided that I don't hear enough differences to necesitate a bunch of sounds. What I do is wire the pickups several ways until I fin 3-5 sounds that I like and then I wire those "usable" sounds onto a 3, 4, or 5 way switch. (Yes, they make a 4 way blade)
But if you want a ton of options, that is honorable as well, just wanted to give some insight to what I have found.
But there are a ton of options theoretically.