Peter Gabriel, Sledgehammer.
Soft Cel, Tainted Love.
Supper’s Ready by Genesis - 7 sections, all quite different
(but Band on the Run was the first one to come to mind)
Styx, Come Sail Away
American City Suite by Cashman and West is - literally - a suite of four songs. There were various radio edits, but even the shortest ones feature three of the pieces. (Some stations played the fourth segment, A Friend Is Dying, as a separate song.
Okay, I’m at a laptop now. Sledgehammer and Tainted Love:
Yeah the rock part in that number is my favourite Who passage - especially Daltrey’s singing and lyrics in that bit.
Speaking of Sab (the reason I came here and the reason I’m starting another thread about it) “Symptom of the Universe” has a distinct three-part heavy beginning / galloping-Iron Maiden / Doobie Brothers song structure. 
There’s a verse added to Billie Holiday’s Gloomy Sunday which is intended to make it a bad dream song rather than a suicide song.
5th Dimension - Age of Aquarius
In this radio edit version, change is at 2:16
The first verse always seemed like it belonged in a different song.
There’s a distinct change of pace/style halfway through “I’ve Seen All Good People” by Yes
Another from The Beatles, “The End”:
And another from Green Day “Brain Stew/Jaded”. They seem like 2 different songs, but always seem to be played together.
Metallica - Master of Puppets (change happens about 3:20):
Harry Chapin’s Taxi has that weird falsetto bit in the middle
There’s a couple of reasons why this first suggestion might be disqualified from this thread.
1- there is a repeated theme
2 - the title’s a bit of a giveaway (though it is a single track on the album Roxy Music)
The Bob (Medley)
Depending how you count them, eight sections in less than six minutes.
Also by Roxy Music, In Every Dreamhome A Heartache
Not a great song, but if you listen for 20 seconds from 2.55 you get to hear the switch.
j
“Rush” by Big Audio Dynamite. About two minutes in, it stops rocking and talks about “Rhythm and melody,” then goes off on a musical tangent unrelated to the rest of the song before returning to the original theme.
From the golden oldies department, I offer the long-forgotten Susan, by the long-forgotten Buckinghams.
The Buckinghhams were a clean-cut group of fellows who specialized in simple love songs, sweetened up with a little brass and strings. And so it was with Susan. For the first 90 seconds, anyway.
At that point, the record producer hijacked a simple little tune and turned it into something resembling the soundtrack of the Starship Enterprise hurtling through the edge of the galaxy. After 30 seconds of a psychedelic extravaganza, the Buckinghams wrest control back from the producer and finish the song.
Radio stations everywhere responded by performing a musicectomy, reducing the song into something the length of an extended jingle.
On Every Street - Dire Straits (the change-up is at about 2:50)
Telegraph Road by Dire Straits has two quite different parts (or three?) Dire Straits-Telegraph Road Live- aLCHEMY Tour 1983 - YouTube