This work introduces a novel single-package optical sensing device for multiple gas sensing, which is suitable for breath analysis applications. It is fabricated on a coverslip substrate via a sputtering technique and uses a planar waveguide configuration with lateral incidence of light. It features three sequentially ordered strips of different materials, which serve to increase the multivariate nature of the response of the device to different gases. For the proof-of-concept, the selected materials are indium tin oxide (ITO), tin oxide (SnO₂), and chromium oxide Ⅲ (Cr₂O₃), while the selected gases are nitric oxide (NO), acetylene (C₂H₂), and ammonia (NH₃). The sensing mechanism is based on the hyperbolic mode resonance (HMR) effect, with the first-order resonance obtained for each strip located in the near infrared region. The multivariate response of the resonances and the correlation with the concentration of each gas allow training a machine learning (ML) model based on a nonlinear autoregressive neural network, enabling the accurate prediction of the concentration of each gas. The obtained limit of detection for all the gases was in the order of a few parts per billion. This innovative approach coined as the multivariate optical resonances spectroscopy demonstrates the potential of HMR-based optical sensors in combination with ML techniques for ultra-sensitive multi-gas detection applications using a single device.