I sometimes see a single word having two trop marks, such as a munach followed by a zakef katan. Usually, of course, words have only one (or are joined to other words and share one, sometimes).
This answer to a question about a shalshelet says, in part:
1) Because it is the first word on the pasuk and deserved a zakef. At this distance from the etnachta, this would be a segolta. But a segolta needs a preceding zarka, and this is the first word. And so it becomes a shalshelet.
Setting aside the specific case (this is not a question about shalshelet), the well-supported answer there says that the trop it should have isn't available because it's not preceded by another. But maybe it could have been, because a word can sometimes have two trops. But maybe it can't have the right ones, or can't have them at that position in the sentence, or something else.
Hence my question: what are the rules governing when a word may, must, or must not carry more than one trop? Are only certain combinations even possible (and if so, which)?
My knowledge of trop is somewhat basic. I know how to lein it (or at least I think I do) at a basic level. I know that a pasuk is usually broken into two parts separated by a "semicolon" like an etnachta, and I know the main "trop families" (e.g. what a full etnacha or zakef katan looks like and what sometimes drops out). I know about conjunctive vs disjunctive trops; if there are gradations within those, or other categories of trop, I don't know those. I don't know much formal theory.