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We identify the simplest combinations of entanglement and incompatibilitygiving the maximum quantum violation for each of the 46 classes of tight Bellinequalities for the (3,2,2) scenario, i.e., three parties, two measurementsper party, and two outcomes per measurement. This allows us to classify themaximum quantum nonlocality according to the simplest resources needed toachieve it. We show that entanglement and incompatibility only produce maximumnonlocality when they are combined in specific ways. For each entanglementclass there is, in most cases, just one incompatibility class leading tomaximum nonlocality. We also identify two interesting cases. We show that themaximum quantum violation of \'Sliwa inequality 23 only occurs when the thirdparty measures the identity, so nonlocality cannot increase when we add a thirdparty to the bipartite case. Almost quantum correlations predict that adding anew party increases nonlocality. This points out that either almost quantumcorrelations violate a fundamental principle or that there is a form oftripartite entanglement which quantum theory cannot account for. The otherinteresting case is the maximum quantum violation of \'Sliwa inequality 26,which, like the Mermin inequality, requires maximum incompatibility for allparties. In contrast, it requires a specific entangled state which has the sametripartite negativity as the W state.

Maximum nonlocality in the (3,2,2) scenario