The present study demonstrates a thorough study of dichlorine monoxide's combined stretching vibrational frequencies (Cl₂ O) with particular reference to its fourth, fifth and sixth overtone transitions. The research proposes a systematic method for modelling vibrational dynamics and frequency predictions utilizing a Lie algebraic framework. The methodology accounts for anharmonicity and higher inter-level coupling modulation, which provides a basis for overtone theoretical interpretation. These results are helpful within the framework of molecular spectroscopy for interpreting the results of experiments with this compound. Such an approach can be generalized to other polyatomic molecules possessing similar vibrational modes.