In the days of film, cross processing meant developing film with the process meant for another kind of film, like shooting Ektachrome (normally processed with the E6 process), and processing it using the C41 process (meant for Kodacolor). Film cross processing sometimes generated striking and strange color phenomena, and other times struck out entirely.
The closest digital analog to cross processing is to invert or equalize individual channels of an image in Photoshop. I post-processed this image using a number of different versions of these manipulated channels, and then reapplied the inversions to the inverted image.
To make this all easier, I’ve written a Photoshop Action that creates multiple duplicates of an image, and then seven different cross-processed versions of the original image so that I can easily see which work best.