  It is shown how to construct a successful co-adapted coupling of two copies
of an $n$-dimensional Brownian motion $(B_1,...,B_n)$ while simultaneously
coupling all corresponding copies of L\'{e}vy stochastic areas $\int B_i
dB_j-\int B_j dB_i$. It is conjectured that successful co-adapted couplings
still exist when the L\'{e}vy stochastic areas are replaced by a finite set of
multiply iterated path- and time-integrals, subject to algebraic compatibility
of the initial conditions.
