  The coefficient of a potential R^4 counterterm in N=8 supergravity has been
shown previously to vanish in an explicit three-loop calculation. The R^4 term
respects N=8 supersymmetry; hence this result poses the question of whether
another symmetry could be responsible for the cancellation of the three-loop
divergence. In this article we investigate possible restrictions from the coset
symmetry E7(7)/SU(8), exploring the limits as a single scalar becomes soft, as
well as a double-soft scalar limit relation derived recently by Arkani-Hamed et
al. We implement these relations for the matrix elements of the R^4 term that
occurs in the low-energy expansion of closed-string tree-level amplitudes. We
find that the matrix elements of R^4 that we investigated all obey the
double-soft scalar limit relation, including certain
non-maximally-helicity-violating six-point amplitudes. However, the single-soft
limit does not vanish for this latter set of amplitudes, which suggests that
the E7(7) symmetry is broken by the R^4 term.
