Although overlapping resonances have been studied extensively in conventional resonance theories, there have not been many studies on them in multichannel quantum defect theories (MQDT). In MQDT, overlapping resonances occur between the channels instead of states, which pose far greater difficulty. Their systematic treatment was obtained for cases involving degenerate closed channels by applying our previous theory, which decouples background scattering from the resonance scattering in the MQDT formulation. The use of mathematical theory on con-diagonalization and con-similarity was essential for handling the non-Hermitian symmetric complex matrix. Overlapping resonances in rare gas spectra of Ar, Kr and Xe were analyzed using this theory and the results were compared with the ones of the previous alternative parameterizations of MQDT which make the open-open part $K^{oo}$ and closed-closed part $K^{cc}$ of reactance submatrices zero. The comparison revealed that separation of background and resonance scatterings achieved in our formulation in a systematic way was not achieved in the representation of $K^{oo};=;0;and;K^{cc}$ = 0 when overlapping resonances are present.