Almost my entire music collection, and the various genres I listen to, have regular shifting tempos, melodies, time signatures, chord progressions, etc, etc.
I listen to various subgenres of prog, jazz, and classical, all of which are well known for doing this.
The opening track from King Crimson's debut album, "21st Century Schizoid Man", after the intro vocal section, goes into a fast tempos jazz influenced frenetic instrumental section with different melodies than the opening and closing, followed by a kind of stuttering tempo, then, quite abruptly shifts back into the original tempo. All the while, shifting between 4/4 and 6/4.
Yes - Close to the Edge changes tempo, chords, time signatures so often, it's hard to keep up. It shits between 12/8/, 6/4, 4/4, at various times, and varies tempos from section to section. Also changes in melody, quiet and loud passages, mood changes.
Genesis - Super's Ready, changes tempos, and time signatures pretty often. There is even a section of the piece titled, "Apocalypse in 9/8". Each section of this song has related, but different melodies.
Mahavishnu Orchestra has so many examples, it's kind of hard to list just one. But, "Dream" is as a good place to start. It starts with a slow tempo section that builds into a very fast section, that slows in tempo again. The melodies also change. I believe it shifts between 4/4 and 15/8. All done with terrifying levels of musicianship.
Return to Forever - Duel of the Jester and the Tyrant (pt 1 and 2) is loaded with tempo, melody changes.
And don't even get me started on the complexity of the tempo, time, and other changes in classical music of the later half of the 20th century, up through the present.
More bands, and musicians known for tempo, melody, time and other changes:
Steve Coleman - contemporary jazz with lots of changes and complex shifting rhythms.
Oregon - long existing jazz ensemble that pretty much defined modern chamber-jazz.
The Contortionist - technical-metal band, with constant changes and complexity, and ridiculous levels of musicianship.
PFM - Italian prog band, with a great deal of tempo and melody changes. Not to mention they could compose some drop dead gorgeous melodies.
ELP, Banco, del mutuo Soccorso, Dream Theater, Panzerballett, Frank Zappa, Gentle Giant, National Health, Happy the Man, Deus ex Machina, Magma... I could go on for pages...