No. It cannot happen. The gods are fickle and jealous. A champion who obtained the mark of a god and then chose to pursue another one would end up as a walking ****** within seconds.
This is why Archaons achievement is so massive. By sheer force of will he managed to obtain 4 marks. He is a big deal for a reason.
The Varanguard example proves this. Individually they are all chaos Lords, with all the personal attachments that comes with. Archaon can over ride that though. He basically let's them worship as they see fit but when they turn up for a shift at work they do what he tells them. If that means putting a shift in with the Slaanesh badge on then so be it.