We further pursue our earlier investigations on a framework for analyzing the dynamics of n-species models of facultative mutualism, providing general sufficient conditions for the global stability of the positive equilibrium. These conditions, consisting of inequalities involving reproductive ratios that are computed at high population densities, augmented by either sublinearity and monotonicity properties, are then observed to be valid for several n-species versions of commonly used models of mutualism, yielding stability criteria with practical relevance.