You can wire all three pickups in series (or any number of pickups, theoretically).
However, the sound is not likely to be that nice.
With that number of coils in series, you would have a very high output, with probably not much high end or upper midrange.
I'd suggest putting series/parallel switches on each pickup, which make a big difference for MM-style pickups.
With those and a volume control for each pickup, you would have loads of tones available without too much difficult wiring.
You could even do the series/parallel on push-pull pots to keep it clean looking.
Also- with a setup like this, you will have to worry about the amount of magnetic force pulling on the string.
You will have to set the pickups further from the strings to avoid this.
Otherwise, the field strength will interfere with the vibration of the string and cause strange tones, odd harmonics etc.