  We consider the large data scattering problem for the 2D and 3D cubic-quintic
NLS in the focusing-focusing regime. Our attention is firstly restricted to the
2D space, where the cubic nonlinearity is $L^2$-critical. We establish a new
type of scattering criterion that is uniquely determined by the mass of the
initial data, which differs from the classical setting based on the Lyapunov
functional. At the end, we also formulate a solely mass-determining scattering
threshold for the 3D cubic-quintic NLS in the focusing-focusing regime.
