There is an interesting sense in which standard polygamy (i.e., polygyny or polyandry) presupposes the binarity of marriage. In standard polygamy, there is one individual, A, who stands in a marriage relationship to each of a plurality of other individuals, the Bs. But the marriage relationships themselves are binary: A is married to each of the Bs, and the Bs are not married to each other (they have a different kind of relationship).
The same would be true with more complex graph theoretic structures than the simple star-shaped structure of polygyny and polyandry (with A at the center and the Bs at the periphery). If Alice is married to Bob and Carl, and Bob and Carl are each married to Davita, the quadrilateral graph-theoretic structure of this relationship is still constituted by a four binary marriage relationships.
Thus, in these kinds of cases, what we would have are not a plural marriage, but a plurality of binary marriages with overlap. This, I think, makes for more precise terminology. The moral and political questions normally considered under the head of “plural marriages” are about the possibility or morality of overlap between binary marriages.
To truly go beyond the binary would require a relationship that irreducibly contains more than two people, a relationship not constituted by pairwise relationships. I think a pretty good case can be made that even if one accepts overlapping binary marriages, as in standard polygamy, as genuine marriages (I am not sure one should), irreducibly non-binary relationships would still not be marriages (just as unary relationships wouldn't be). The structure of the relationship is just radically different.