A systematic study of simultaneous optimization of constraint satisfaction problems was initiated in [BKS15]. The simplest such problem is the simultaneous Max-Cut. [BKKST18] gave a 878 -minimum approximation algorithm for simultaneous Max-Cut which is {\em almost optimal} assuming the Unique Games Conjecture (UGC). For a single instance Max-Cut, [GW95] gave an G W -approximation algorithm where G W 87856720 which is {\em optimal} assuming the UGC.It was left open whether one can achieve an G W -minimum approximation algorithm for simultaneous Max-Cut. We answer the question by showing that there exists an absolute constant 0 1 0 − 5 such that it is NP-hard to get an ( G W − 0 ) -minimum approximation for simultaneous Max-Cut assuming the UGC.