We theoretically proposed and experimentally demonstrated that a nonlinear acoustic dimer system with amplitude-dependent and sign-reversible coupling exhibits unprecedented control over multistability and state selection. The engineered inter-resonator coupling $\kappa ={\kappa }_0+\alpha |{\psi }_1{|}^2$ yields a quintic steady-state response with at most three dynamically stable states: low (LS), intermediate (IS), and high (HS). Monotonic sweeps produce asymmetric hysteresis—$\mathrm{LS}\to \mathrm{HS}$ on upsweep, but $\mathrm{HS}\to \mathrm{IS}\to \mathrm{LS}$ on downsweep—leaving a linearly stable yet dynamically inaccessible IS under conventional driving. Basin-of-attraction analysis shows that nonlinear coupling reshapes the phase-space geometry, creating barriers that isolate the IS. Leveraging this insight, we developed a simple up-down-up adiabatic protocol that achieves full and selective access to all stable states, including the otherwise transparent IS. Mapping versus drive frequency and damping reveals transitions from separated bistable loops to a unified tristable regime. These results, to our knowledge, provide the first experimental realization of nonlinear-coupling-governed multistability and a versatile route to programmable multistate control.

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• Acoustic metamaterials
• Nonlinear acoustics
• Coupled oscillators
• Hamiltonian systems
• Nonlinear waves
• Acoustic techniques