In the simultaneous Max-Cut problem, we are given k weighted graphs on the same set of n vertices, and the goal is to find a cut of the vertex set so that the minimum, over the k graphs, of the cut value is as large as possible. Previous work [BKS15] gave a polynomial time algorithm which achieved an approximation factor of 1-2- op1q for this problem (and an approximation factor of 1-2 + ϵk in the unweighted case, where "k Ñ 0 as k Ñ 8). In this work, we give a polynomial time approximation algorithm for simultaneous Max-Cut with an approximation factor of 0:8780 (for all constant k). The natural SDP formulation for simultaneous Max-Cut was shown to have an integrality gap of 1-2+ϵk in [BKS15]. In achieving the better approximation guarantee, we use a stronger Sum-of-Squares hierarchy SDP relaxation and a rounding algorithm based on Raghavendra-Tan [RT12], in addition to techniques from [BKS15].