  We consider the Cauchy problem for the nonlinear Schr\"odinger equation with
double nonlinearities with opposite sign, with one term is mass-critical and
the other term is mass-supercritical and energy-subcritical, which includes the
famous two-dimensional cubic-quintic nonlinear Schr\"odinger equaton. We prove
global wellposedness and scattering in $H^1(\mathbb{R}^d)$ below the threshold
for non-radial data when $1 \le d \le 4$.
