Stomach sleepers typically need a soft or thin pillow. However, if you sleep with more of your chest on the pillow, you tuck your arm under the pillow or you sleep on the corner of your pillow you may need a medium or thicker pillow.
Many stomach sleepers that sleep with an arm under the pillow also like to sleep on the corner of their pillow. Typically, pillow corner stomach sleepers don't like to have the pillow come up around their face when sleeping on their stomachs so they position their heads on the corner while tucking their arm. Due to the fact that traditionally designed pillow taper, are thinner, in the four corners you may need to increase your pillow density or thickness choice one density level so the pillow corner is as thick and supportive as it can be.
Do you, like so many, tuck your arm under your pillow while sleeping on your stomach? It's actually very common but most are not doing it to prop up their heads with their arms while sleeping on there stomach. Typically stomach sleepers tuck their arm under the pillow because it creates so much strain on your neck when your arm is alongside your body. If you're an 'arm-tucker' you may need a soft thin down pillow so that you when you do tuck your arm you don't create an even more uncomfortable spine angle with it tucked.