I loved The Affair. I think this could work if the viewpoint each time was markedly different. It would take some getting used to from a readers point of view. But writers have attempted stranger things and got away with it.
I have songs that are relevant for my main characters. DI Amelia Barton’s was Various Storms and Saints by Florence and the Machine. DI Jack Kent’s seems to be Sinnerman by Nina Simone (Felix da Housecat version). No idea why - maybe because it’s got the word rock in it.