Can more than one coordinating conjunction (and, but, or, etc.) be used in a sentence?
For example: "It was never my intention to become wealthy, but opportunities seemed to just happen, and I was not about to refuse them."
It is perfectly fine to use multiple conjunctions in a sentence, and although it may produce something which seems a bit verbose, there are appropriate uses for it, and in literature in particular, it's commonly used to create a sense of continuity throughout a scene by forcing the reader to take in the entire paragraph without stopping, and Ernest Hemingway was famous for doing precisely that!
Admittedly, my crude attempt was not nearly as good as Hemingway's.
This is a literary technique. I definitely wouldn't advise it for technical writing or any formal communication. It makes the reader work a lot harder to read your sentences than would otherwise be necessary.