As ‘always’ @tav has a solution with his stacks. If you look at the demo page, it shows images that have some animation happen on ‘hover’ (e.g. show some text). The elements can be still clicked, which then can open a new page or likely a modal as well (here Andrew’s Limelight stack will likely work, too).
http://sectionspro.bigwhiteduck.com/box/hover-captions/
Edit: wrote my response before checking your link. You’re looking for a more intricate solution, where the image is replaced by multiple buttons, each changing the modal. There was a recent discussion of ‘flip’ stacks where an image can be flipped, and the ‘backside’ will be displayed, which can be any stacks again. Such a stack in combination with limelight should get you to your goal.
The thread was ‘Switching content without Controllers’