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As these systems continue to expand in scale and functionality, investigating their potential vulnerabilities has become increasingly important. However, existing studies on adversarial attacks in multi-agent systems primarily focus on isolated agents or unimodal settings, leaving the vulnerabilities of MM-MAS largely underexplored. To bridge this gap, we introduce HAM$^{3}$, a Hierarchical Attack framework for multi-modal multi-agent systems that decomposes attacks into three interconnected layers. Specifically, at the perception layer, HAM$^{3}$ mounts attacks by perturbing visual inputs, textual inputs, and their fused visual-textual representations. 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