Ok, solution: will take the tip from Guest CJ way up the thread and sit on the opposite side of the room from my friend. When she starts a song, I can join in, and then, when it comes to my turn, vice versa, So now it's as Guest on 26.09.19 suggested, and let other folk join in if they want: I don't mind that so long as they don't try to take over the song by changing time signature, key or tempo. (We've all been there, I guess!)

And, slight thread drift, excuse me for that, but it's also about people making assumptions. At some singing events I've been to, there is an MC who picks and chooses people to sing, but seems to only pick those he/she knows. By definition, at this sort of event, at least 90% of people there are singers, with just a very few being "only here to listen". There IS time to fit everyone in, if only the MC would ask that vital question "Is there anyone who wants to sing, who hasn't sung yet?" But no, they go back and ask those with better-known faces (to them!) to sing again. I really do find this practice objectionable, especially after the MC has introduced the session as being "a chance for everyone to sing".