In many cases, watch factories modify these base calibers and sell them under their own name. While I was working my way through the "Uhrenkatalog" to compile the "manufactories" list, I noticed that the catalog usually lists both the proper caliber name and the caliber on which it is based, and I thought that you might be interested in this information. It might even influence your buying decisions when you are interested in a certain caliber.
You should, however, consider that a company modifies these calibers when it gives them their own name and decide what is important for you. Such modifications may include a new balance, usually include hand finishing of plate and/or bridges and in some cases, the base caliber is really only the "base" to which some additional functions are added.
This point is impressively illustrated when you look at Chronoswiss C.732 in comparison to its base caliber ETA/Valjoux 7750: There is a world of difference! In C.732, the calendar disc is removed, hour and minute hands are placed excentrically, and, above all, Chronoswiss adds their own patented modifications to make it a split second chronograph ("chronographe rattrapante").
Do not overestimate the term "base caliber" - the differences can be enormous!
One company should be mentioned here for its excellent information policy: Oris includes detailed information about all movements in their "High Mech Booklet," and they are not afraid to publicly state that, e.g., the Oris 640 is based on the ETA 2836-2. (By the way: I have an Oris "Big Crown" with a 640 - the watch is not a certified chronometer, but it is accurate to one second per day! Careful finishing of large series calibers can produce extraordinary results.) It would be nice if other companies would follow Oris' example!