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Epsilon-near-zero (ENZ) metamaterials represent a powerful toolkit for selectively transmitting and localizing light through cavity resonances, enabling the study of mesoscopic phenomena and facilitating the design of photonic devices. In this experimental study, we demonstrate the feasibility of engineering and actively controlling cavity modes, as well as tuning their mutual coupling, in an ENZ multilayer structure. Specifically, by employing a high-birefringence liquid crystal film as a tunable nanocavity, the polarization-dependent coupling of resonant modes with narrow spectral width and spatial extent was achieved. Surface forces aparatus (SFA) allowed us to continuously and precisely control the thickness of the liquid crystal film contained between the nanocavities and thus vary the detuning between the cavity modes. Hence, we were able to manipulate nanocavities anti-crossing behaviors. The suggested methodology unlocks the full potential of tunable optical coupling in epsilon-near-zero metamaterials and provides a versatile approach to the creation of tunable photonic devices, including bio-photonic sensors, and/or tunable planar metamaterials for on-chip spectrometers.