If I understand correctly, I think I came across a Brackey's youtube tutorial awhile back demonstrating a similar technique. You can have two completely different environments, but see through the door as if it's a portal. Thus you could set up your skybox-like magic dr.strange room, and your normal room and use something like this demo.
If not, I'd imagine you can achieve something similar with render textures.
If still not, you can get more complicated with camera layers and the new physics worlds api. But i'd avoid that if something like the Brackeys video is good enough!
In case the video becomes unavailable, the process is as follows:
Set up two identical rooms that aren't visible to each other. You can do this by putting them on different layers, and modifying which layers the player camera can see.
In the center of each room you put a door. The door has a render texture and a trigger in the doorway. Each room has it's own camera which renders the view from the doorway into the other room onto a render texture. In room A's door, put the render texture from the camera in room B's door, so the doorway in room A is showing a view of room B. Do the same but the other way around for room B. Move the cameras around so as the player moves relative to the door, the view also changes.
When you hit the trigger of the doorway, teleport the player and it's camera to the corresponding spot in the door of the other room. You probably also want to temporarily ignore the trigger so the player isn't immediately teleported back.
This whole effect gives the illusion of a magic dr strange door.