Who needs mp4 and the mystery meat data within? Kornel Lesiński’s lossygif compresses GIF images, including animations, at the cost of noise. Though GIF does not offer true lossy compression, superimposing long horizontal lines of identical pixels gets the job done before encoding. Photoshop already does this, but this is better at it and it’s free.
See also Gifski, the author’s high-definition GIF movie encoder. It does the exact opposite thing, manipulating the GIF format into showing thousands of colors per frame at the cost of massive file sizes.