Overprinting can create an interesting aesthetic value through screen printing designs. It can be replicated through digital print, but the unique outcome of the hand-rendered process gives a desirable quality when it comes to selling and exhibiting typographic design.
This particular example is nothing spectacular in terms of design composition, but it demonstrates the interesting relationship between the red and the cyan when overprinted. Interestingly, these colours are used to create stereoscopic images, where overprinting is a necessary process for the 3D effect to work.
Although they're not screen printed, these digital images demonstrate an overprinted outcome, using it to take less emphasis off the red foreground - allowing the background image to stand out more.