Yes and no.
Yes because it's possible, but no because technically when you want to do this, you are lexicalizing one of them and then adding on the [pre|suf]ix to that base word and so are no longer strictly using a prefix and a suffix together.
So in the case of mononess, you aren't referring to a singularity of quality, rather the quality of being one/singular, so mono- is lexicalized as mono1 to which the suffix -ness is added. I could perhaps understand someone talking about the preness of something (the quality of coming before, or pre- + -ness), but I think I'd definitely need a hyphen to actually mentally decompose the word properly.
In the case of mononess though, it's a bit hypothetical, since the word oneness is already regularly used for the concept. In fact, I reckon most any combination will likely be better served by some other word or phrasing.
1. I'm ignoring the fact that apparently mono is already an adjective mainly because its glosses are monochrome and monophonic which don't apply here (that and I've neither seen nor used it)