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UTe₂ is a promising candidate for a time-reversal symmetry (TRS) breaking superconductor. Since the recent discovery of its superconducting state below 1.6 K, several studies have established its spin-triplet character (e.g. a high upper critical field, and a negligible change in the Knight shift across T_c). A field trainable Kerr rotation even indicated TRS breaking of the superconducting order parameter. Because TRS-breaking superconductivity requires a two-component order parameter, and because UTe₂ is orthorhombic, two separate superconducting transitions are expected. Two transitions have indeed been observed in heat capacity measurements. However, these findings are heavily debated. We investigate the possibility of two superconducting transitions with resonant ultrasound spectroscopy and look into what this can tell us about two-component order parameters.