Reducing staff numbers in LilyPond

[Ken Williams]

I have a choral piece where some of it is 4-part divisi SATB, and some of it is unison (true unison, not octaves). I would love to notate this in LilyPond with the two (women's & men's) staves combining visually into one staff - when in the middle of a printed line, I'd like it to actually converge to the single staff, something like this (which I just pasted together crudely in an image editor):

https://i.stack.imgur.com/FV0Q5.png

Is that possible in LilyPond?

(BTW - I originally posted this as https://music.stackexchange.com/questions/62569, and did get one response but I still don't quite get how I'd go about this - I get the impression the mailing list is more well-trafficked?)

 -Ken