The answer is 'No'. You can not add people to someone else's photo. Only the person who uploaded the photo can tag people in it. There are two places where you can tag other person on Instagram i.e. in the caption and in a comment. If you want to add someone in a caption, just type @ sign followed by the username. That person will get notification from Instagram that you have added him. Another way to use tags is in the comments. You can easily reply to someone's comment on a photo. Tap and hols the username and select 'Mention user' option. You will be able to reply directly to that person's comment or caption.