Interactions of the Great Cycle Spirits
Source: A book of Esoteric Knowledge
Looking for behavior resembling teams
The book doesn't have anything on Dragon as a Cycle Spirit, or Whale, but among the spirits listed:
There is nothing resembling a team of more than two; it's all individual relationships, and they are not symmetric.
Dog could probably be described not too inaccurately as an ally of both Bear and Crane. Bear might be an ally of habit with Dog; Crane is more aloof.
Monkey is perfectly happy to actively support both sides of a conflict. So is Tiger, for different reasons.
Fox aims for no one having grudges with her, rather than close ties.
Monkey is the only one that is possibly believed to have some ability to "cheat" in agreemnts, though it may be that bargains tend to have more wiggle room and odd loopholes.
Spider is known for making agreements that turn out have hidden benefits for himself, but everyone is used to that.
Butterfly and Spider don't get along.
Dog and Fox don't get along.
Serpent and Tortoise more subtly don't get along.