I refer specifically to the 2016 version, but this should also apply to 2013 and 2010.
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Microsoft has deemed PowerPoint unworthy of a macro recorder for lo these many versions (I think it was dropped in either 2003 or 2007 from memory), so no help can be obtained from there.
The linked MSDN "help" item is woeful. It states that the property returns a Master object, though that isn't relevant for the moment.
An Office support page describes a slide master here. A Slide Master seems to be where the presentation's Slide Layouts live, presumably in the SlideMaster's CustomLayouts property, though it's interesting to note that only the first 9 of those CustomLayouts correspond to what you see in the GUI. (I count 11 CustomLayout objects in the SlideMaster in a new, blank presentation.) The numbers change if you add new layouts though the two vertical text layouts never seem to appear in the GUI list. This too is not the problem.
The problem is that you can in fact have more than one Slide Master per presentation by going to the View menu, Slide Master, and then selecting Insert Slide Master. Having multiple Slide Masters is discussed on the Office Support site here.
Frankly I regard this functionality as slightly broken because if you do that, then apply a Theme to the new Slide Master, you end up with a third Slide Master; the original under "Office Theme", a second under "Custom Design", and a third under the name of the Theme that you applied. This too is not in itself a problem. (Though it's worth noting that a Presentation does not have an AddSlideMaster method, which means that it does not seem to be possible to do this by VBA. Not that you necessarily want to, but if you did, you can't. There is only an .AddTitleMaster method which seems to be useless since all presentations have a TitleMaster as far as I can see and if a presentation has one then that method will error out according to the documentation.)
The problem is that the Presentation object does not have a collection of Slide Masters. It has only that one property, SlideMaster, which returns a single Slide Master / Master object.
Accordingly I can't see any way that you can programmatically add a new Slide Master. And even if you used one that is added through the GUI you can't seem to access any Slide Master except for the first one. And therefore you don't seem to be able to access, manipulate or assign any Layout from any Slide Master other than the first one to an individual slide.
Am I correct in this assumption, or am I missing something?
I shall offer thanks in advance even though that is often deleted from questions. Not that this one is likely to attract much attention; I suspect that there may be another Tumbleweed badge in my future.
Perhaps this page will be helpful in understanding it better - http://skp.mvps.org/2007/ppt003.htm