  In this paper we set up a theory of two-matrix weighted little BMO in two
parameters. We prove that being a member of this class is equivalent to
belonging uniformly in each variable to two-matrix weighted (one-parameter)
BMO, a class studied extensively by J. Isralowitz, S. Pott, S. Treil and
others. Using this equivalence, we deduce lower and upper bounds in terms of
the two-matrix weighted little BMO norm of the symbol for the norm of
commutators with Journ\'e operators.
