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The promotion of collinear classical spin configurations as well as theenhanced tendency towards nearest-neighbor clustering of the quantum spins aretypical features of the frustrating isotropic three-body exchange interactionsin Heisenberg spin systems. Based on numerical density-matrix renormalizationgroup calculations, we demonstrate that these extra interactions in theHeisenberg chain constructed from alternating S=3/2 and sigma=1/2 site spinscan generate numerous specific quantum spin states, including somepartially-polarized ferrimagnetic states as well as a doubly-degeneratenon-magnetic gapped phase. In the non-magnetic region of the phase diagram, themodel describes a crossover between the spin-1 and spin-2 Haldane-type states.

Alternating-spin S=3/2 and sigma=1/2 Heisenberg chain with three-body exchange interactions