<p>In this work, we develop a systematic formalism to evaluate the upper bound of a large family of holographic entanglement entropy combinations when fixing <i>n</i> subsystems and fine-tuning one other subsystem. The upper bound configurations and values of these entropy combinations can be derived and classified. The upper bound of these entropy combinations reveals holographic <i>n</i> + 1-partite entanglement that <i>n</i> fixed subsystems participate in. In AdS₃/CFT₂, AdS₄/CFT₃, and even higher-dimensional holography, one can, in principle, find different formulas of upper bound values, reflecting the fundamental difference in entanglement structure in different dimensions.</p>