I don't find two singles in series to be as interesting a sound as parallel. If I were adding a fourth sound to a Tele, I'd probably go with the Jerry Donahue fake-Strat setting.
Ok you got me interested, what's this?
It's a little resister and cap wired in to put the pickups partially out of phase (don't ask me to explain; I'm not knowledgeable enough) and get something akin to positions 2&4 on a Strat.
I've been fascinated by it for twenty years, but still haven't gotten around to actually doing it.
Do you have a diagram with values?
Also, If you go back far enough in the Forum, there's an Artie diagram in a very old thread of mine, back when I was obsessed with getting as many sounds out of a single guitar as possible.
Jerry Donahue Wiring.
Position ONE:
The neck (Strat®) pickup with the tone circuit OUT, affording a clearer, brighter tone
to compensate for the inherent dullness normally found in this position. The result: a lead guitar
sound that echoes the blues shadings of Clapton, Hendrix, etc.
Position TWO:
The neck (Strat®) pickup with the tone circuit IN, allowing the guitarist to soften the tone
for rhythm or mellow leads, as per a stock Tele rhythm pickup.
Position THREE:
The neck and bridge pickups are in the standard stock parallel wiring with the tone circuit IN,
enhancing the customary Tele® sound.
Position FOUR:
By combining both pickups with a capacitor and resistor in a controlled degree of reversed phase,
the guitar offers a bell-like, rich tone that echoes the classic Strat® sound. Until now,
this sound could only be obtained by the use of the bridge and middle pickups on a typical Strat.
Position FIVE:
An updated stock-style bridge pickup with symmetrically staggered pole pieces for great string
balance and a special wind for increased sustain. It captures that great old Tele® lead sound
that launched post-War popular music in America, and has the same gutsy, "punchy" tone of Jerry's
prized '52 Tele®. By the way, the Fender® Custom Shop Jerry Donahue Signature model uses a
Seymour Duncan APTL-3JD Jerry Donahue Model bridge pickup and an APS-2 Vintage Flat pickup
for Strat® in the neck position. In any event, the wiring is fairly complex and the key to the
Strat® sound is using a Strat® pickup in the neck position.

I think you might be talking about this diagram.
Maybe I'm conflating things. You did a diagram for a Nashville Tele with, like, 11 settings or something dumb. But maybe it didn't include the JD mod.
Two vintage-output single coils sound pretty cool in series. It is a thicker sound that is a good contrast to parallel. I wouldn't do it with more powerful pickups, as it will turn to mud pretty quickly.
I've got series on my Danelectro (about as low-output as they come). It's... Fine? I haven't bothered to change it. But I def prefer the middle settings on my other guitars more. ¯\_(ツ)_/¯
I don't want muddy. What's the output on the vintage pickups?
I don't want muddy. What's the output on the vintage pickups?
Compare to the Duncan vintage offerings. Series single coils sounds pretty tubby. That does work sometimes, especially into a fuzz. It also works if you are the only guitarist in the band, and need to take up a lot of space.