C. S. I. Jenkins has an interesting paper at Ergo called "Modal Monogamy" which concerns the position that the only possible romantic love relationships are dyadic and exclusive (that's the 'modal monogamy', which is a horrible name for it). Jenkins argues (correctly) that such a view is both poorly motivated and inconsistent with actual facts about human behavior. One could add, I think, that it involves a conception of how love works that is dubious at best -- this idea that love is like a pipe between people, hermetically sealed off and easily discernible from all the other pipes. In reality, love by its nature diffuses and reflects onto other loves, and is refracted into different kinds of love. We see this quite clearly with other kinds of love than romantic love. Love of mother and father is not perfectly separable from the love they have for their children, for instance. Even if we stay at the level of purely romantic relationships, this self-diffusion of love is one of the very things that requires regimentation of relationships by custom and mutual understanding in the first place -- to keep it from diffusing badly.
In the course of the discussion, Jenkins suggests, although no more than suggests, that it is reasonable, given all of this, to conclude that (romantic) love is a multigrade relation. A relation is unigrade if it always has the same number of relata ('adicity' is the technical name for this number). Thus 'x is after y' is a binary relation; afterness will be a unigrade relation if every case of afterness is a binary relation. In topology, betweenness is a ternary relation ('x is between y and z'); it is unigrade because this always has to be the case. A relation is multigrade if it can relate a different number of relata in different circumstances. So if romantic love is multigrade, and R is the relation of mutual romantic loving (I add the 'mutual' because it simplifies things somewhat for exposition), we could have one case of L(x,y), 'x and y are related by loving (each other)', and another case in which the relation is L(x,y,z), 'x, y, and z are related by loving (each other)', where this is not taken just be shorthand for L(x,y) & L(y,z) & L(x,z).
I think Jenkins's suggestion is, in fact, correct of the actual relation of romantic love, and true of love in general, in fact. A parent loves his or her child; suppose he or she has another child; it makes no sense to count 'loves of children', and say that he or she has added a new and distinct love of child to a previous love of child. A friend loves a friend; suppose a new friend of them both joins them, now a Three Musketeers; this is not in any way adequately analyzable into each person having two loves-of-a-friend. Romantic love is not any different, whether the result happens to be tragedy, farce, or something else. (Jenkins pretty clearly has active polyamory in mind, as in n. 16, but there are obviously many other ways one can end up in such situations, including many in which one did not intend or want to end up in such a situation.)
There are a number of relations that seem to be very difficult to analyze in a purely unigrade way. For instance, very general relations, because they are very general: Let R be the relation of being related; then you can have R(x,y), R(x,y,z), R(w,x,y,z), and so on for any number of things -- and it has to be the same relation that can have all of these adicities. Interpersonal relations often also seem to be resistant to analysis entirely in terms of unigrade relations; because human beings are capable of structuring their relationships with each other in highly complicated ways.
There are arguments that all relations should be either unigrade or at least reducible to unigrade relations, but I've yet to come across a good one. The main one I know of, for instance, which is based on work by David Armstrong, manages both to confuse self-identity with identity across situations and to beg the question by treating adicity as intrinsic to all relations. Perhaps somewhere there's one worth taking seriously, but I've yet to find it. And the prima facie evidence against the idea is quite strong.