In Illustrator I have the same linked file being used in three different layers. The linked file is an .eps that contains a simple pattern. Now if I want to use a different pattern, is there a way to simply say "use this other file in these three layers instead of the current one"?
Open the Links panel under Windows -> Links. Select each link you want to relink with a new file. CTRL click to select more than one item from any part of the list or hold Shift if you want to select more than one item and the items are listed consecutively in the selection box.
Click the relink (chainlink) icon in the Links panel. A new window will open where you can search for a new file. You will have to do this with each linked file.
Each eps that you have will stay in the same location according to the Layers panel.