In principal, YES, there is. I developed some commercial software to do 'injection of content' into HTML, on-the-fly, using a proxy (http only).
A common usage scenario is the injection of ads, typically overlays, by means of injected JS.
In case of interest, contact me augustus_meyerATyahoo.com
You should do this in the login page only, inserting your own content into 3rd party sites you have no control over is a bad idea. The target site may style or overlay your content or your content could break key features of the website. I've not once encountered MITM content injection where I thought "This adds a lot of value to my internet experience and isn't distracting me from what I want to do".
Injection of content into 3rd party pages can help in funding free hotspots. You are correct, that there _might_ be interference, but only in case of extremely dynamic (tricky) sites.. Which need to be blacklisted.
MTs 'interstetials' are much more risky regarding disturbance of 3rd party sites.