It's an entirely different base.
There's a seller on ebay, whose username is Nicade, that had a couple NOS 4-way bases up recently.
I don't think they sold.
The 4-way base has a diamond shaped hole in the top of the base, vs. the round one on an 8-way.
The 4-way also uses a slightly smaller actuator.
I think the 4-way actuator was included with the bases on that auction.
If not, I'm sure he has a bunch laying around.