Group role assignment(GRA) is originally a complex problem in role-based collaboration(RBC). The solution to GRA provides modelling techniques for more complex problems. GRA with constraints(GRA~+) is categorized as a class of complex assignment problems. At present, there are few generally efficient solutions to this category of problems. Each special problem case requires a specific solution. Group multi-role assignment(GMRA) and GRA with conflicting agents on roles(GRACAR) are two problem cases in GRA+. The contributions of this paper include: 1) The formalization of a new problem of GRA+, called group multi-role assignment with conflicting roles and agents(GMAC), which is an extension to the combination of GMRA and GRACAR; 2) A practical solution based on an optimization platform; 3) A sufficient condition, used in planning,for solving GMAC problems; and 4) A clear presentation of the benefits in avoiding conflicts when dealing with GMAC. The proposed methods are verified by experiments, simulations,proofs and analysis.