Doctor Strange: 7 Tony Stark Cameos That Would Rule
4. They Meet At The Hospital
This idea is less concerned with the Strange side of things, and more with the Doctor part.
For all the more otherworldly elements this film is going to have, it's main character is still a working doctor, and we will see him in action at a hospital.
So, could one of his patients be a certain Tony Stark? Since he has that Arc Reactor in his chest, there is potentially cause for him to visit a hospital from time to time, and it'll need someone incredibly skilled to perform any procedures involving it.
That, then, could be the case for the meeting between the two. If there are two credits scenes - one mid, one post - then it makes sense that one will be somewhat connected to the film we've just watched, and probably presented in a more lighthearted fashion. In slightly similar fashion to Stark on the couch talking to Bruce Banner, we could find him in hospital being operated on by Dr. Stephen Strange.