We propose a new family of relaxation schemes for mathematical program with complementarity constraints that extends the relaxations of Kadrani, Dussault, Bechakroun from 2009 and the one of Kanzow & Schwartz from 2011. We discuss the properties of the sequence of relaxed non-linear program as well as stationarity properties of limiting points. A sub-family of our relaxation schemes has the desired property of converging to an M-stationary point. We introduce a new constraint qualication to prove convergence of our method, which is the weakest known constraint qualication that ensures bounded-ness of the sequence generated by the method. A comprehensive numerical comparison between existing relaxations methods is performed on the library of test problems MacMPEC and shows promising results for our new method. Numerical perspectives shows an enhanced version of the buttery relaxation to mathematical program with vanishing constraints.