In this letter, precoding for max-min fairness (MMF) for multi-group multicasting with a common message is studied. The MMF problem is converted into a weighted mean square error minimization problem. A rate-splitting solution is proposed. In rate-splitting, multicast messages for each group are divided into private and common parts, and these common parts, together with the original common message are combined as a \emph{super common} message. This super common message is superposed on or concatenated to the private multicast data vector, or it is transmitted via a mixed scheme. Simulations show that RS demonstrates significant gains especially in overloaded systems.