I have run a few multi-team fights. Here are a few tendencies I go for.
A Defend action probably means they are defending against all-comers regardless of their opposing action: the team rolls defend once and it is used independently or vs against opposed actions.
An Attack action probably means they are directing it against a specific team and ought to tell which. Other opposed action are compared against the same Attack result even if it was not directed at that team.
A Feint action probably means they are directing it against a specific team and ought to tell which. Other opposed actions are compared against the same Feint result even if it was not directed at that team.
A Manuveur action is probably directed at all-comers but offers its benefit to only limited degree: the success can be applied to either one of the teams which were unable to counter or the one team which was unable to counter (or to the Manuveuring team in the case of Gain Position).
Two patrol mice teams Attack and Defend against a single animal team’s Feint - animal team rolls Feint, but it is not applied against Attackers and Defenders do not test. Defenders take reduction of Dispo from Feint; animal team takes reduction in Dispo from Attack.
Two animal teams Manuveur and Attack against single patrol mice team’s Defend - animal teams help each other (I would probably have the Manuveur test with helper from Attack) while patrol mice roll Defend. Test is versus.
Two animal teams Feint and Defend against two patrol mice teams’ Attack and Manuveur - teams need to state targets; animal Feint tests independently against Manuveur and will be target of successful Manuveur; animal Defend tests versus Attack and will be target of successful Attack. This 2 vs 2 could go a variety of ways, and my example is sparse.
If the mice have split into two teams to defends a group of squirrels being attacked by snakes, the squirrels might not be attacking the mice, so maybe ought not be a team. If the two animal teams are not opposed to each other, they maybe ough tto simply be a large team.
Keep in mind that the 2 vs 2 team battle is probably only going to occur if there is a really big scene going on. In such a condition, I would probably break down the situation to have two distinct conflicts and hand-wave the result of NPC teams in conflict with each other (or maybe roll that out privately and consider the lasting impact of their resulting compromise for the future of the adventures).
I would do all I can to avoid having a 2 vs 2 teams scenario; because, it is inherently more difficult to manage and increases the load on the compromise. Scenarios of 2vs 1 or 1 vs 2 is not so terribly difficult, but the teams must have distinct battle lines drawn as to why they want different things.