  In this paper, we present two multiple scalar auxiliary variable
(MSAV)-based, finite element numerical schemes for the Abels-Garcke-Gr{\"u}n
(AGG) model, which is a thermodynamically consistent phase field model of
two-phase incompressible flows with different densities. Both schemes are
decoupled, linear, second-order in time, and the numerical implementation turns
out to be straightforward. The first scheme solves the Navier-Stokes equations
in a saddle point formulation, while the second one employs the artificial
compressibility method, leading to a fully decoupled structure with a
time-independent pressure update equation. In terms of computational cost, only
a sequence of independent elliptic or saddle point systems needs to be solved
at each time step. At a theoretical level, the unique solvability and
unconditional energy stability (with respect to a modified energy functional)
of the proposed schemes are established. In addition, comprehensive numerical
simulations are performed to verify the effectiveness and robustness of the
proposed schemes.
