  We extend our analysis of the soft behaviour of string amplitudes with
massive insertions to closed strings at tree level (sphere). Relying on our
previous results for open strings on the disk and on KLT formulae we check
universality of the soft behaviour for gravitons to sub-leading order for
superstring amplitudes and show how this gets modified for bosonic strings. At
sub-sub-leading order we argue in favour of universality for superstrings on
the basis of OPE of the vertex operators and gauge invariance for the soft
graviton. The results are illustrated by explicit examples of 4-point
amplitudes with one massive insertion in any dimension, including D=4, where
use of the helicity spinor formalism drastically simplifies the expressions. As
a by-product of our analysis we confirm that the `single valued projection'
holds for massive amplitudes, too. We briefly comment on the soft behaviour of
the anti-symmetric tensor and on loop corrections.
