  We address special cases of the analogues of the exponential algebraic
closedness conjecture relative to the exponential maps of semiabelian varieties
and to the modular $j$ function. In particular, we show that the graph of the
exponential of an abelian variety intersects products of free rotund varieties
in which the subvariety of the domain is a sufficiently generic linear
subspace, and that the graph of $j$ intersects products of free broad varieties
in which the subvariety of the domain is a M\"obius subvariety.
