I think that the working premise of a 3- or more party relationship might best be found in terms of a D/s (Dominance/submission, or alternatively, M/s - Master/slave) relationship where one or more Doms control/own/love one or more submissives/slaves.
One such family I know of personally has a Master, three Sirs, and about seven or eight submissives, about half of whom are permanent live-in slaves.
The slaves/submissives honour and care for one another in their submissive roles, and in turn worship and attend to the wishes of their Sirs/Master (this being the expression of their love for them, while the Sirs/Master look after the well-being of not just their particular subs/slaves, but after the well-being of the others' subs/slaves as well, with the Master more or less caring after everyone in his household.
It is an interesting thing to observe, especially when they are following strict protocol, but even in loose protocol the respect and love are noticeably present - like a brotherhood with discipline and kink.
It is probably that same discipline and structure that lends itself to the relative success of such a multi-dimensional relationship, whereas a more conventional relationship has to address the equality of the partners much more carefully.
Which is not to say that equality of men in a D/s family is completely disregarded - it is just that the roles of everyone in that family are clearly established and boundaries are provided and deeply respected.