Using synchrotron radiation in the tender X-ray regime, a photoelectron spectrum showing the formation of single site double-core-hole pre-edge states, involving the K shell of the O atom in CO, has been recorded by means of high-resolution electron spectroscopy. The experimentally observed structures have been simulated, interpreted and assigned, employing state-of-the-art ab initio quantum chemical calculations, on the basis of a theoretical model, accounting for their so-called direct or conjugate character. Features appearing above the double ionization threshold have been reproduced by taking into account the strong mixing between multi-excited and continuum states. The shift of the σ* resonance below the double ionization threshold, in combination with the non-negligible contributions of multi-excited configurations in the final states reached, gives rise to a series of avoided crossings between the different potential energy curves.