Hi,
One more twist in the present discussion is the word like "preposterous."
As far as I know,
pre- is a prefix
post- also is a prefix, Yes, but not in this case, see below.
and -ous is the suffix.
Then where is the Base?
The word is derived from the Latin 'prae', meaning 'before', and the Latin 'posterus', meaning 'next'. While it's true that 'post' is often used as an English prefix, here it is not. In effect, here it is the base of the word. The semantic idea of the word is that something 'before the next' sounds absurd and unnatural, although when I think about that, I'm not sure that I agree. However, I didn't invent the word.
Best wishes, Clive