I can't begin to describe how terrible an explainer I am
So I'll portray my thoughts through song images using the Spectre as an example: 
In this scene there are three Spectres and a Lost Soul named Goldilocks. However for this case to work the Spectres aren't being rendered to the main scene but a sample texture accessible to a post-processing shader.
Example sample texture:
It's important that all other items including level geometry be rendered black, both in front and behind of the Spectre (or other chosen sprites/textures). This basically gives the post-processing shader "hot spots" it can use to manipulate the main scene.
Photoshop re-enactment:
More advanced stuff can be done by colour encoding replacement sprites and tweaking the shader further.
This sprite sheet allows the shader to smoothly bend the sprites' edges to connect to the scene (Blue channel), give body contours to the warping (Green channel) and also center the effect on each sprite individually, giving the impression of multiple shader passes (Red channel). And with this method it opens up the possiblity for a translucent Lost Goldilocks to be able to affect the warping amount depending on it's own alpha value.
Some thoughts:
I propose that there be an option to still render the sprite into the main scene so that glass can have a texture and not just be warping air.
It would be good to have a couple destination sample textures so that modders can combine a few custom effects like warped glass and steam in one level (ooh steamed glass!).
I'm sure I've glossed over some things here but hopefully it sort of made sense
