Oh, neat, this mentions my patch to rust-brotli! FWIW, I do not, an never have, worked for Dropbox. ;-)
A similar tool would be possible for gzip - I made one a long time ago that could append a literal stored block to the end of a gzip stream.
One note about brotli - appendable chunks after the first will generally have a worse compression ratio because they can't reference brotli's built in preshared dictionary, but my use case was appending a small amount of dynamic data to an otherwise static file, where this isn't a significant problem.