I suppose that Happiness is a Warm Gun doesn’t qualify, as it’s four seperate songs stuck together.
Tainted Love/Where did our love go? by Soft Cell
Black Magic Woman / Gypsy Queen by Santana
(Peter Green / Gabor Szabo)
As well as Time/Home
I think that Paul Simon’s* Homeless* is made up of two seperate songs.
Village People : San Francisco / Hollywood
If pravnick can include BOTR, the Proud Mary most definitely has the feel of two different songs.
On “Alive Behind the Green Door,” Flogging Molly has a song “De-(That’s All Right)-Lilah”, a combination of Tom Jones and Elvis Presley tunes.
Sloan’s “Suppose They Close the Door” off Navy Blues transitions back and forth between two entirely different songs.
Grateful Dead did it all the time with a bunch of songs. The set that comes to mind is China Cat---->I Know You Rider
“Width Of A Circle” by David Bowie.
My Chemical Romance – Welcome to the Black Parade
“Paradise By The DashBoard Light” by Meat Loaf.
“Dead and Gone” by Gypsy has two distinct melodies.
They also did Scarlet Begonias and Fire On the Mountain as a song suite quite often. Not to mention Not Fade Away / Going Down the Road Feeling Bad that actually made it onto the Skullfuck Lp.
Jefferson Airplane had “Won’t You Try / Saturday Afternoon.”
CSN had “Suite: Judy Blue Eyes” which was an amalgamation of two partial songs.
And for something completely different, Patti Smith did a cover version of Van Morrison’s "Gloria’ that is intertwined with wholly original lyrics & music (“Jesus died for somebody’s sins, but not mine…”) as well as “Horses”, a long song-suite that incorperates music & lyrics from the mid-60s proto-punk hit “Land of 1000 Dances” (don’t remember who did it originally.)
“You Set the Scene” by Love is two songs combined into one.
How about “Fingertips”, by They Might Be Giants? Twenty-one separate songs in about four and a half minutes, listed under a single title.
I’ve heard that “Frankenstein” by Edgar Winter Group got its name because it was bits of several unfinished songs, sewn together.
Abacab by Genesis got its name because when it was being written they had A, B and C parts, and the name of the song is the order in which the segments were eventually assembled.
“A Quick One While He’s Away” by the Who is a suite of several songs.
“Scarborogh Fair/Cantacle” by Simon and Garfunkel are two songs, and they end up being sung simultanously.
Irving Berlin’s “An Old Fashoned Wedding” from Annie Get Your Gun does the same thing; Berlin was known to mix tunes in counterpoint.
Procul Harum had “In Held 'Twas in I” – named after the first words of the five songs that make it up.
And there’s Harry Neilson’s version of You Can’t Do That, which contains at least a dozen (and some sources say over 20) Beatles songs.