Multi-colored linocuts can be done with a single or multiple plates, but in aquatint, there's not single plate option (unless you count a la poupee). However, the concept of printing one color at a time in perfectly aligned layers still applies. After etching a basic line drawing, that image can be transfered to a number of additional plates, which are each aquatinted for a specific color. Once the plates have been made, it still takes some playing around to find the exact color inks needed for the desired effect.
This technique is what my instructor, Anita Toney, focuses on herself. I'm also inspired by Sarah Newton's awesome aquatint and recently got to see one of her multiple plate pieces up close.