This is an amplification to a point made to irishsultan in the comments to Monty de Sade.
I'm more certain now:
Variants 2 and 4 are the same with respect to the switches and stays, you just win a goat as well as a car if you get it right and you get nothing if you get it wrong.
Note that the options each of the move variants are based on the distribution illustrated in the "Just Leave the Gap" variant.
irishsultan seemed concerned about the placements of the goats. The image below relates to a slightly different variation of Monty de Sade in which we do care about the names of the goats, so a grouping of Mary with the car is distinct from a grouping with Ava with the car.
Therefore we now have the following options:
A = Ava, B = Mary and Car
A = Mary, B = Ava and Car
A = Car, B = Ava and Mary
A = Mary and Car, B = Ava
A = Ava and Car, B = Mary
A = Ava and Mary, B = Car
(Where Ava just short for "the door behind which Ava is hidden", etc)
The result is still a likelihood of 1/2 of winning by switching or staying..