The theme is
The Beatles
One was a star.
The best was bested.
One drove a car.
One only rested.
Ringo Starr. Pete Best was replaced. Either Drive My Car (vvye) or Day Tripper (Sunday driver, yeah). While there is a lot of sleeping in Beatles songs, I'm Only Sleeping (vvye) also includes "only".
One made art.
With stones they vied.
But then they did part.
And half of them died.
Stuart Sutcliffe, original bassist, left to be an artist (A E), They were a group at the same time as the Rolling Stones, then they broke up and now two of the four (Harrison and Lennon) are dead
31 was a cop.
Mustard's bank was his nose.
They rose to the top.
As your matriarch knows.
In Maxwell's Silver Hammer, "P.C. 31 said we caught a dirty one." (Irishpanda) - PC for Police Constable, or cop, Mean Mr Mustard "Keeps a ten-bob note up his nose", the Beatles were the top band by any measure, and Your Mother Should Know
Of the last two,
One is amazed.
The other sells shoes.
The youth were all crazed.
This is Paul McCartney, who sang Maybe I'm Amazed, and Ringo Starr, who now has a line of shoes (among other things). The last line is Beatlemania (A E)
They all shared a liver.
They spoke of her love.
Iron met river.
And villainous glove.
pun on Liverpool where they were from (histocrat), She Loves You (A E), Liverpool's Cast Iron Shore mentioned in Glass Onion (Irishpanda), in Yellow Submarine bad guy's fiercest weapon was "The Dreadful Flying Glove"
A lane full of sights.
The town had a pool.
Three members, one knight.
A silvery tool.
Penny Lane, pun on Liverpool where they were from, all four were awarded MBE but John returned his, Paul was knighted, and Maxwell's Silver Hammer
Fabulous number.
A half dozen cried.
Eyes gilded in slumber.
We heard of a slide.
"Fab Four", though there's plenty of weeping, in While My Guitar Gently Weeps (A E) the six strings of the guitar can be the half dozen, Golden Slumbers, and Helter Skelter
A teacher was killed.
And broken wings flew.
A door was filled.
And you're wealthy too.
Maxwell's Silver Hammer is about a teacher being killed (Fillet), a line in Blackbird is take these broken wings and learn to fly, in Fixing A Hole: "I'm filling the cracks that ran through the door" (Irishpanda), Baby, You're a Rich Man.
An apartment was burned.
Or so it was said.
Because a lover was spurned.
With a drain in his bed.
Norwegian Wood (This Bird Has Flown). "I crawled off to sleep in the bath" and "I lit a fire."