Mashes wouldn't count, do they? Or not mashups as we know it, because what about "Tainted Love/Where Did Our Love Go?" by Soft Cell? I mean, already they're doing a cover song, and then they transition into a completely different one?

Paul McCartney loved to do this in the early 70s -- Band on the Run is another example.

Is there a word for this sort of thing?

Well, I'm having a hard time for that. Mostly because it's much bigger than pop songs. Compositions that change key, tempo, and tone go back a pretty long time and you can find them all over the world. European art music took it to the Nth degree, and you can also find it in classical musics of India and Indonesia and China and, I'm sure, lots of other high art musical styles. It's also always been really common in jazz.

I think what you're thinking about might be the infusion of the rock-and-roll/bluesgenre with ideas from high-art music. The thing that made rock and blues stand out when they were new was that they were such vernacular styles, building on simple repetitive structures from folk music (in the sense of the people's non-high-art music). They imported this stripped-down simplicity into the pop genre and it overwhelmed popular culture. But beginning in the mid-1960s, when a lot of people started getting high-minded about their rock music, and a lot of people with the benefit of musical education were getting involved in becoming pop artists, the idea of complexifying rock and pop came along. First there was the bridge, which has become practically standard in pop-rock George Martin, for instance, really pushed the Beatles in this direction, and their songs are loaded with bridges. Then there are things like "Golden Slumbers" or "A Day in the Life" where you can really see the Beatles assembling fragmentary lyric/melodic segments into long songs that morph a few times.

This movement became more self-conscious and more common in the 70s. The influence of psychedelics probably helped. By the time you get to Yes and the Moody Blues, you hear a lot of songs that go through several stages and change quality several times. People have called it "Art Rock" and it's a basic compositional feature of the progressive genre that has also been employed by people interested in pushing their songwriting boundaries a little bit farther than the potentially stale "verse, chorus, verse, chorus, bridge, verse, chorus" structure.

So:

Starship Trooper, And You and I, All Good People - Yes
Tuesday Afternoon, The Question - The Moody Blues
Dark Side of the Moon - Pink Floyd
Stairway to Heaven - Led Zeppelin
Skating Away, Thick as a Brick, Aqualung - Jethro Tull
Lots of Rush, lots of Phish, lots of Frank Zappa, early Genesis
Dust in the Wind, Carry On My Wayward Son - Kansas
4th of July Asbury Park, Jungleland - Springsteen

...you could make a wicked long list. I guess my point is that it's more than a feature of a few songs, it's a compositional technique that a lot of different kinds of pop musicians have exploited, starting mostly in the late 60s.

Fiona Apple - Fast As You Can changes time signatures very abruptly several times.

Arguably my favorite song on arguably my favorite record does this - "Sue Egypt" on Captain Beefheart & the Magic Band's Doc at the Radar Station.

The word that occurs to me is "derail."

Yep, I thought of Paul McCartney too, and the changing time signatures in "Happiness is a Warm Gun" and, as Miko said above "A Day in the Life".

Ha! And TPS was using my laptop last night, and I forgot to log back in. That was me.

Also: Paranoid Android by Radiohead (original and U Mass cover).

(I still have Doc at the Radar Station on vinyl. I have to convert it because I need to hear Dirty Blue Gene with all the pop and crackles from the original instead of a new, clean digital version.)

Ha! And TPS was using my laptop last night, and I forgot to log back in. That was me.

A-ha! That explains her talking about putting shoes on the kid in the other thread. I thought it sounded like you!

Yeah, I didn't realise last night, obviously. TPS was babbysitting the Mad-Dog.

Layla

Meatloaf - Paradise by the Dashboard Light

Blue Oyster Cult - Don't Fear the Reaper

I automatically gravitate to songs with multiple changes like these, but am not familiar with any term for it.

I am reminded of an early Grateful Dead album that had different names for the different changes in the same song. In order to get more publishing royalty points on the album, the opening track "That's It For The Other One" was artificially divided into four other "songs" by the band:

* "Cryptical Envelopment"
* "Quodlibet for Tenderfeet"
* "The Faster We Go, The Rounder We Get"
* "We Leave the Castle"

Happiness is a Warm Gun = A/B/C/D song form. Rather unusual in pop music.

"Good Vibrations" by the Beach Boys. It's a string of basically unrelated fragments. (Some other BB songs, too, but this is the best example.)

Brian Wilson referred to it as "modular" songwriting.

"Happiness is a Warm Gun" is a Lennon song, not McCartney.

I know. I skipped where I explained that thinking of McCartney makes me think of the Beatles and thus the Lennon song. Because although I know, I don't really care who wrote it. It's the Beatles. I expect that's bad.

Also, there are some Arcade fire songs that do this, but I don't really know the band so I don't know the songs.

McCartney just wrote snippets and then threw them together.

Others:
The Who, "A Quick One While He's Away"
Boston, "Foreplay/Long Time"