Under the framework of Filippov solutions, passivity analysis of memristive BAM neural networks with multi-proportional delays can be guaranteed by constructing suitable Lyapunov-Krasovskii functional, Jensen's inequality, Lemma of Schur Complement, the theory of set-valued maps and functional differential equations with discontinuous right-hand sides. Moreover, the terms of multi-proportional delays are deformed by nonlinear transformation in this paper. We have successfully established sufficient conditions for the passivity of BAM memristive neural networks with multiple proportional delays. These conditions not only reveal the relationship between system parameters and passivity, but also provide theoretical basis and guidance for designing stable, reliable, and well passive BAM memristive neural networks. Finally, two numerical examples are exploited to show the effectiveness of the derived LMI-based passivity conditions. The work presented in this article not only deepens the understanding of the dynamic behavior of BAM memristive neural networks, but also provides a new perspective for the design and optimization of this type of network in practical applications.