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Vibrational strong coupling of molecules to optical cavities based on plasmonic resonances has been explored recently because plasmonic near-fields can provide strong coupling in sub-diffraction limited volumes. Such field localization maximizes coupling strength, which is crucial for modifying the vibrational response of molecules and, thereby, manipulating chemical reactions. Here, we demonstrate an angle-independent plasmonic nanodisk substrate that overcomes limitations of traditional Fabry–Pérot optical cavities because the design can strongly couple with all molecules on the surface of the substrate regardless of molecular orientation. We demonstrate that the plasmonic substrate provides strong coupling with the C=O vibrational stretch of deposited films of PMMA. We also show that the large linewidths of the plasmon resonance allow for simultaneous strong coupling to two, orthogonal water symmetric and asymmetric vibrational modes in a thin film of copper sulfate monohydrate deposited on the substrate surface. A three-coupled-oscillator model is developed to analyze the coupling strength of the plasmon resonance with these two water modes. With precise control over the nanodisk diameter, the plasmon resonance is tuned systematically through the modes, with the Rabi splitting from both modes varying as a function of the plasmon frequency and with strong coupling to both modes achieved simultaneously for a range of diameters. This work may aid further studies into manipulation of the ground-state chemical landscape of molecules by perturbing multiple vibrational modes simultaneously and increasing the coupling strength in sub-diffraction limited volumes.