It helps to understand that the word "emulsion" is a tad over-extended in use. Cyanotype and salted paper (Van Dyke, the 'browns', Pt/Pd) solutions are called emulsions but they are actually very thin liquids that soak right into the paper. The only way to increase the native d-max is to apply multiple coats and the paper type makes a tremendous difference.
Gelatin-based processes (silver gelatin and carbon) sit on top of the paper they are coated on. The thickness of the emulsion can be controlled by both the amount of gelatin used and by the temperature of the emulsion or glop when it is applied to the paper. If you want a thicker coat you don't have to apply multiple layers, you simply cool the emulsion down a bit, or start with a recipe with a higher gelatin content. In fact, each layer introduces coating artifacts -- usually considered flaws, although that is strictly an artistic judgment, not a strictly technical one. As a matter of personal taste, I don't care for sloppy coating, but ymmv. A good emulsion, coated at the right temperature needs only one layer. Paper choice is important. You want a good wet strength and a texture and color that appeals to you, but beyond that, silver gelatin is much more forgiving of paper choice than the thin-only emulsion processes.