Create a member or contact field that can be populated with links to other members. This can be used to describe multiple kinds of relationship. It can be used to indicate spouses, siblings, parent/child, guardian, program sponsor, dependent.

I see it as a many-to-many relationship.

My specific use case is "sponsorship".
Bob sponsors Ted and Andrew.
Frank sponsors Ted and Erik.

which also can be written as:
Ted is sponsored by Bob and Frank
Erik is sponsored by Frank
Andrew is sponsored by Bob.

Being able to select multiple people could be accomplished using something along the lines of the existing Group "Manage Participants" screen.