A reflexive pronoun refers to the subject, not a subset or a superset of the subject.

A first- or second-person object pronoun which is the same person and number as the subject (je me …, je … à moi, nous nous …, nous … à nous, etc.) is automatically reflexive. Unlike the third person in French, and unlike languages such as English that allows things like “we … us” as opposed to “we … ourselves”, the first and second person in French don’t have a distinct non-reflexive form, and any possible non-reflexive meaning (where the two “we/us” or the two “you” refer to different sets) is so rare that it would not be understood.

For example, in “nous nous regardons”, both occurrences of nous refer to the same set of people. This sentence can have two different meanings: either all of us are looking at all of us, or each of us is looking at himself or herself. But if myself and Alice are looking at the whole team, it’s impossible to convey this without using something more explicit than nous.

Whichever nous comes first in the sentence must be clear from the context. If there’s a second nous, it refers to the same set of people as the first. So to express a different group, it’s necessary to use a noun, not a pronoun. For example:

Alice et moi avons les yeux ouverts. Nous regardons l’équipe.

Alice et moi pensons que notre équipe n’en fait pas assez. Nous allons surveiller l’équipe.

(Note that regarder can’t mean “watch” in this sense.)

It would be the same in the third person. A reflexive pronoun cannot work since it doesn’t refer to the same thing as the subject. A non-reflexive pronoun can work if it isn’t ambiguous.

Alice et lui pensent que l’équipe n’en fait pas assez. Ils la surveillent.   (La is grammatically ambiguous: it could refer to either Alice or the team. But the only plausible meaning is that Alice and him are watching the team, not that Alice and him are watching Alice.)