I suppose you could speculatively decompress and then re-compress and see if you get the original compressed file back, and maybe most people happen to use the same compression implementations with default settings.
This puts a serious limitation on your compression. You would only be able to re-do the entropy coding part of DEFLATE, which is actually pretty good.
You would still need to store the original Huffman tables for each block, so you can reconstruct the entropy coding exactly.
I doubt this would even gain you a single percentage.
[1] https://github.com/deus-libri/preflate
[2] https://github.com/schnaader/precomp-cpp/ (which internally makes use of preflate)
EPUB is an example of this. They're mostly bog-standard ZIP archives, but in order for the file to be valid, the "first" file in the archive, linearly speaking, must be named "mimetype" and stored with no compression (each file in a ZIP archive can have a different compression level). If you just unzip an EPUB and then just dumbly zip it back up again, your end file will not be a valid EPUB.