Recent publications by Zielinski and Hanley and by Alsoy and Duda have proposed relationships between self- and mutual-diffusion coefficients in multicomponent systems that can be derived from Bearman's friction-based theory. Subsequently, Zielinski and Alsoy published an article calling into question the ability of these new theories to satisfy the Onsager reciprocal relations, and Nauman and Savoca also reported that the Zielinski and Hanley theory can, in some cases, fail to satisfy material balance constraints. Here, the existing friction-based theories are reviewed and then previous approaches to relating self- and mutual-diffusion coefficients are generalized. The result is an expression that both unifies previous results and is itself a previous result. This generalization prompts us to address the issues raised regarding the existing theories. Some example calculations are also presented, and some directions for future areas of research are suggested.