Replace 3 speed auto with 4 speed ?

[Helge Wunderlich]

I have a 1984 Audi 100 with the 087 3 speed automatic transmission.
The transmission is going bad, and replacement with a used unit seems
to be the best solution. However, since the 3 speed is known to be
less than durable, I' like to try a 4 speed from the later model.

Will a 4 speed transmission fit as a replacement to my 3 speed 087 ?

I am aware that I'd have to change some parts inside the car. How
about the drive shafts ? Any other parts ?