Please forgive me for asking again.
I had the same thing in mind at first.HOwever, my friend finds it strange ( And I think she has a point).
It's because when you try to understand 'taking a picture' literally, it means
( take a picture= I hold and click the camera myself)
Mainly the reason why she said it's strange to say
' Can I take a picture with you.'
jUst to confirm...
take a picture= general idea of taking pictures, to shot pictures.
If you want to be strict, you can say 'Can I have my picture taken with you / our picture taken together?', but I think that many native speakers would as likely ask a friend to 'take a picture with them' (two of them together in the frame, with a passerby operating the camera-- to whom, by the way, they would say, 'Could you take our picture?'), without bothering about the logic of the matter.
Other members may have other opinions.
PS: If you wish to continue a conversation, Lisa, especially with the same person, you should continue to post on the original thread rather than start a new one. I just stumbled upon this one by accident.