User blog comment:BlueBarracudaMary/Protagonist, Deuteragonist, Tritagonist, Tetartagonist, Pentagonist, What Comes Next?/@comment-33286367-20200124014244/@comment-961279-20200124095738

Those really don't make sense. The character Liam might be a deuteragonist in a technical sense for writing of the movie, but in the movie, he's Max's son, not "Max's deuteragonist".

And to clarify, when you label these characters as deuteragonists, do you mean that there are two equally-important main characters, or do you mean that they are less important than the main character(s)?

Same goes with tritagonist. Three equally-important characters, or this character is less important than two other characters? Whichever way it is, "secondary tritagonist" then means either:
 * "This is one of three equally-important characters but they are actually less important than the other two."
 * "This is a character who is third-most important, but they are even less important than that."

Same goes with hexagonist. Does it mean there are six equally-important characters, or this is a sixth-most important character. If Peppermint Patty is not a hexagonist but a "secondary hexagonist", is she among the six most-important characters but actually less important than the other five, or is she a sixth-level character of importance who is even less important than that?

Labels like this over-complicate things and lead to confusion because the usage is inconsistent. It also leads to contradictions when qualifiers like "secondary" and "tertiary" are added ("they're at this specific level yet not really because they're even lower").

Keep it simple. Main character(s), secondary character(s) and minor character(s). There's no need to go any further. Spend time seeing what makes the character a PERSON instead of a label.