  We prove a multilinear local $T(b)$ theorem that differs from previously
considered multilinear local $T(b)$ theorems in using exclusively general
testing functions $b$ as opposed to a mix of general testing functions and
indicator functions. The main new feature is a set of relations between the
various testing functions $b$ that to our knowledge has not been observed in
the literature and is necessitated by our approach. For simplicity we restrict
attention to the perfect dyadic model.
