Adding many layers of paint or primer is perfectly fine, as long as you properly prepare the original surface, use light coats and follow recommended drying times/conditions for the material, and properly prepare fresh surfaces between coats as necessary for appearance or proper adhesion (as specified by the manufacturer of your product).
There is nothing wrong with doing a few coats of primer, sanding each smooth between coats and removing the sanding dust/oils with alcohol. This if preferable if you going for a smooth look and high gloss or buffed finish. Your paint will only be as flat and smooth as whatever is under it.
My process for painting anything "perfectly" is/would be as follows:
Fill all dents, dings, voids, etc as necessary and sand smooth using a reasonably hard block. You may need multiple coats as your filler dries and you sand it. Sand the whole case well with 220-320 paper using a block wherever possible. Wipe case down well with naptha or alcohol on a rag.
Prime the case, spray edges of a part then spray the whole part immediately. Sand primer smooth with 320-600 grit paper. Repeat process until the parts are completely primered after sanding (no burned through edges) and the primer has filled any pin-hole blemishes, pits, etc. If you have an area that needs thicker primer, such as deeper scratches, pitting, etc, feel free to spray several coats on that area without sanding, but, make sure the primer is dry between coats. Thicker takes much longer to dry. If you rush it, it will not sand well adn will take longer to dry than if you simply waited longer between coats. Again, repeat this and earlier priming+sanding steps as necessary.
Wipe down case with alcohol on a soft rag (unless you used a water-based product then follow manufactures diferctions). Regardless of any companies directions, do not ever use a tack cloth, any commercial tack cloth, to remove dust. They often casue more harm than good.
You final primer sanding should use 400-600 grit paper and be doen with a block everywhere possible. No matter how careful you are, you fingers will leave different pressure and sanded areas and will eventually lead to subtle striping in the paint layers.
Paint with several coats, following manufactures directions for environmental conditions and time between coats. Usually, you can do 2-3 light coats of paint without sanding in between if you observe the correct timing. This is because paint will marginally dissolve the layer below if it is not too cured, thus forming a chemically structured thicker layer.
Depending on the appearance, dust in the environemnt, your skills with a spray gun or can, the brand of paint used, spitting from dirty nozzels, intention to polish and buff, etc, you may be happy or you may need to sand with 600-1000 grit, preferably wet sanding it, always using a hard rubber block, and then spray again.
With paint, as with primer, remember to spray the edges well then immediately spray the part.
Remember, you most recently applied coat of paint will only look as good as all previous coats/surface quality below. You can never spray paint to cover a run, sag, dent, or any other blemish. All you can do is apply enough paint to that area to allow you to sand it out without burning through, without applying so much paint that it dries improperly and produces a weaker, more chip or blush prone final product.
Its not that hard though, you just have to be patient and realize the preparation is critical for a truly excellent finish.