Can somebody tell me why a Nikon D5200 would restrict the multiple exposure shots to 2 or 3 ? Is it some design issue or something else?
There is no real reason. Digital cameras could in theory cope with much more images. A number of models allow up to 9 but that is the most I've seen. The good ones allow you to confirm and retake each shot which makes this immensely workable.
In any case you can do multiple exposures simulated yourself in most image manipulation software such as Photoshop. The advantage there is that you control the blending and alignment.
As with most software features, including bracketing, manufacturers tend to provide what they think the target market will use and are careful not to diminish sales of higher end models.
A multiple exposure mode takes a given number of exposures and those are stored each in its own file on memory card. After the set is complete the in-camera program processes them into a single multiple exposure image. So, in reality, there is no "true" multiexposure happening inside your camera, but quite the same process as what you would be doing with your editing software in computer.
After the exposures are fused in camera the resulting image is written to a file on memory card.
I'd guess Nikon D5200 simply has an amount of internal memory that allows for two or three exposures only. Or some obscure marketing point?