The two Vanishing Points (yellow and purple lines, I think?) in this image are not on the same Horizontal Plain. We have been calling this “Split Perspective,” but so far have not been able to find the official terminology. (The image is a screen shot from the film “French Kiss.”)
A misconception here, I say! The perspective of the image is what the camera has made - a mathematical mapping from 3D scene to 2D image. It hasn't any special short name, a name like 1, 2 or 3 point perspectives, which you obviously have heard. It's the result of camera placement, where it is aimed to, film size, the used lens and what's in front of the camera.
Those 1, 2 or more point perspectives are drawing construction aids. Many scenes such as streets and buildings around them have in 3D space parallel line sets. Imaging mathematics say that in 2D the images of a bunch of parallel lines should point towards common vanishing point. Only those lines whose vanishing points are far out of the image area can be drawn as parallel without making a big error.
If you say "this drawing has 3 point perspective", it means it has been constructed by having 3 vanishing points. If you say "This photo has 3 point perspective" I think you see that accurate enough replica of it for your purposes can be drawn by having 3 vanishing points.
I bet you see that vertical lines in this photo do not need a vanishing point due the horizontal aiming of the camera and narrow vertical viewing sector. That can be helped artificially by tilting the lens or film or it's perspective straightening with software.
But you have drawn yellow lines, violet lines and green lines which converge to 3 points. Also red lines seem to have a vanishing point so near that you have taken it into the account. Unfortunately your colored line bunches do not all present sets of in 3D parallel lines, so I wouldn't call this an attempt to draw help lines for perspective drawing at all. Fix few lines (=recolor those which are not parallel in 3D, but obviously present horizons in differently tilted planes), then it will be.
There are an infinite number of vanishing points, every point in your viewing field is a vanishing point.
But as in our modern societies, we are used to constructing orthogonal things (at 90°) walls, rooms, boxes, furniture, streets, we are used to seeing specifical vanishing points at those angles relative to each other.
Each line has its own vanishing point; when we see several lines "aligned", the street, the lines of the window, the stairs, the rooftops... we enforce that perception.
In this specific case the street is not leveled, one is simply going in another direction, besides that it seems that the corner is not a 90° street but a diagonal one.
But there is another element. There are some types of photos that cover more viewing field than a normal one, using either wide or ultra-wide lenses. As our species is a hunter type both of our eyes need to gather the info just in front of us. Some other species are used to see the surroundings, like birds, deers, and fishes.
And there are also programs that stitch together different images, and we can have some 360° view on one single image, search for example "Equirectangular Projection" https://wiki.panotools.org/Equirectangular_Projection
In this specific case, you can do this "effect" on a normal 90° street using these techniques.
The point is that the perspective is already there, for example to your left and right side, but you do not see them normally. Stitching these photos you can. Here is a little old paper I made for a 3D community.
Take a look at these other two posts: