Some people, although listening to another's kidush (Friday night), sing part of it along with him: specifically (in my experience), the lines starting "ki vanu vacharta" when recited with this tune. This seems to me arguably not to be a problem (see e.g. Mishna B'rura 690 s'if katan 13–14; but see the comments on this question). But I'm wondering whether there are any sources that discuss the issue.
As always, for practical halacha, consult your rabbi.