  Our previous paper introduces topological notions of normal crossings
symplectic divisor and variety and establishes that they are equivalent, in a
suitable sense, to the desired geometric notions. Friedman's d-semistability
condition is well-known to be an obstruction to the smoothability of a normal
crossings variety in a one-parameter family with a smooth total space in the
algebraic geometry category. We show that the direct analogue of this condition
is the only obstruction to such smoothability in the symplectic topology
category. Every smooth fiber of the families of smoothings we describe provides
a multifold analogue of the now classical (two-fold) symplectic sum
construction; we thus establish an old suggestion of Gromov in a strong~form.
