The Unforgiven and The Unforgiven II by Metallica

Subway to Sally have a pretty popular song called Traum vom Tod II (Dream of Death 2). Took me years to find Traum vom Tod I.

Rise Against's I Was A Teenage Anarchist feels a lot like a sequel to their Baby, I'm An Anarchist.

The first track in the album "diamond mine" which is a collaboration between Scottish singer King Creosote and producer John Hopkins. Absolutely fantastic album through and through but the first track is just ambience from a Scottish pub with the music very slowly coming in until it eventually seamlessly transitions into track 2 which is the "most famous" from the album. Just perfect.

Tim Armstrong was a guest on Bad Religion's Television, on Stranger Than Fiction. So I've always wondered if Radio by Rancid was a follow-up.

Destiny Potato - The Buildup. It establishes most of the motifs used in Indifferent one track later on the same album.

Dream Theater has a song called Metropolis Part 1. Originally they didn't plan to have any additional parts, but it worked out that eventually they decided to follow it up. Instead of a single song, they did a whole album: Metropolis Part 2: Scenes from a Memory. And I think it's their best work.

Sandstorm by Darude has a song right before it on his album called "the calm before the storm" and I actually enjoy it quite a bit.

Primus has the four Fisherman's Chronicles songs.

1. John the Fisherman
2. Fish On
3. The Ol' Diamondback Sturgeon
4. Last Salmon Man

Another thing that might count as an example is that Wings' Band on the Run and Helen Wheels both mention a character named Sailor Sam.

Edit: Added to post.

They're not that popular compared to Pink Floyd or David Bowie, but there's a band called The Dear Hunter that have 5 albums called Act I through Act V that are one continuous story of a guy's life.

So in that sense every song on those albums are a sequel and prequel to every other, but some of the musical themes and motifs are more obviously reintroduced, referenced, and re-applied in new contexts as the albums go on.

They have albums that aren't those 5, which are not in the canon, by the way.

David Bowie wrote a continuation to "Space Oddity" ("Ashes to Ashes") and the original also inspired a few songs by other artists that directly reference it ("Major Tom (Coming Home)" by Peter Schilling, "Hallo Spaceboy" by Pet Shop Boys).

GUNSHIP

Tech Noir
Tech Noir 2

The Decemberists

The Crane Wife 1 & 2
The Crane Wife 3

The Unicorns

I Don't Wanna Die
Ready To Die

Handsome Boy Modeling School

Look At This Face (Oh My God They're Gorgeous)
Modeling Sucks

Basically all of King Gizzard and the Lizard Wizard's discography.

Rush: Cygnus X-1 books I and II. More of a two-part story, but kind of fits the question.

Tool - Parabol / Parabola Tool - Intermission / Jimmy (although probably among their less popular songs)

Metallica has the unforgiven, unforgiven 2, and unforgiven 3

From the band Grandaddy (across about 15 years of releases):

Jed the Humanoid Robot

Jed's Other Poem

Jeddy 3's poem

Jed the 4th

The Smashing Pumpkins- “1979” and “Perfect”.

People said “Perfect” sounded so much like “1979” that the music video was intentionally made to be a sequel to the latter.

EDIT: The Smashing Pumpkins are my favorite band. If you can find a copy of Greatest Hits Video Collection (1991–2000) (a DVD collection of music videos and other goodies; acted as a companion to Rotten Apples), I recommend it. There is extensive audio commentary on the videos. For example, Stéphane Sednaoui who directed “Today”, claimed to had never listen to the song before the first day of filming. “1979” in particular had master tapes got destroyed after someone left them on the roof of their car, so the entire video had to be re-shot. “Perfect” commentary, Corgan makes the connection to the similarities with “1979”; all but one of the original teenage actors from the first video returned. There is a short film version of “Try” that featured a different ending to “Try, Try, Try”. A few live recordings are included, among them “Fuck You (An Ode to No One)” from the final Metro show when they broke up and “Geek USA” (a special mix that utilized maximum volume on the audio system).

Radiohead's Creep, My Iron Lung, and All I Need

Ozzy had "Crazy Train" and also "A.V.H." which contained the lyrics

Riding on a train that I can't control

One might say such a train was... crazy.

Megadeth with Hanger 18 and later in their career Return to Hanger.

The Killers- “Mr. Brightside” and “Miss Atomic Bomb”

It may not seem obvious but “Miss Atomic Bomb” is intentionally a sequel. The music video even tells a story that is a continuation of the “Mr. Brightside” video, with Izabella Miko and Eric Roberts reprising their roles.

Not sure if this counts because it’s on the same album but on The Mountain Goats album Transcendental Youth starts with “Amy (AKA Spent Gladiator)” and the second to last track is “Spent Gladiator 2.”

Also, their album Jenny From Thebes is a sequel to their album All Hail West Texas.

Also also, there are a number of songs early in the discography that are about the same couple, culminating in the album Tallahassee.

Anecdotally, I've heard The Police's Synchronicity II on the radio way, way more than Synchronicity I. They're both bangers though.

I just recently learned that Mother Mother released "Hayloft II" in 2022, 14 years after the banger "Hayloft"

I'm not sure if this exactly fits what you're looking for, but the following 5 albums by The Dear Hunter are connected through a shared storyline ^[1]^:

1. Act I: The Lake South, The River North ^[2]^
2. Act II: The Meaning of, and All Things Regarding Ms. Leading ^[3]^
3. Act III: Life and Death ^[4]^
4. Act IV: Rebirth in Reprise ^[5]^
5. Act V: Hymns with the Devil in Confessional ^[6]^

ELP's Karn Evil 9 is a pretty epic trilogy.

The first impression part 2 is what got played most often on the radio, but personally i think part 3 is where it shines.

The Blood Brothers’ “Celebrator” flows very well into the final song on the album, “Devastator”!

360 and 365 from Brat By Charli xcx

Also, Haken's full albums Virus and Vector are prequels to the song Cockroach King from their album The Mountain.

Electric Six has a song called Gay Bar Part Two, the context was purely ironic but it still counts

For that song I wouldn't have chose these two parts. I would've gone for Part 1 and Part 3. Instead of a sequel Part 2 feels like a separate installment if you get what I mean.

Plus that's kind of cheating. Is every prog song split into multiple parts considerable for this? Like also from Pink Floyd, Wish You Were Here (the suite?) is split into two large sections, and the folksy Pigs on the Wing acts like a storybook introduction and ending split into two parts and put at the start and end of the album.

There's a ton more examples like that. Especially on concept albums. The Beach Boys'/Brain Wilson has Wonderful, Song for Children (Look), Child is Father of the Man, and Surf's Up exploring the same idea and building on top of one another.

I'm pretty sure that The Killers have two songs like that, with Mr. Brightside being followed by Miss Atomic Bomb.

Opeth - Patterns in the Ivy and Patterns in the Ivy II. The latter is so beautiful, could've easily been on BWP too imo

Falco's Jeanny and Coming Home.

The Prodigy - Omen(Reprise)

It depends if an ouverture counts, and how popular of a song.

Bad Religion has Ouverture before Sinister Rouge. They are different tracks but they merge together.

Also, one could argue that most of the songs on the album American Idiot by Green Day, are a prequel to the next one. The songs can be separated but they are parts of a story.

Thomas D. of the German hip hop group Die fantastischen Vier has added more and more songs to his warrior trilogy over the years.

1. Krieger
2. Millionen Legionen
3. Mein Schwert

This might be a stretch. Mute - Walking on a Thin Line, which is the end of the album Remember Death, is the direct prequel to the song Resistance which actually starts the album. Its like it's there just to get you to listen to the whole thing again. Which you should. Its really good.

Empty spaces > What shall we do now?

"What shall we do now?" Is basically the part 2 of "Empty Spaces" but was removed from the album as it wouldn't fit the vinyl.

The song is still present in the film, and a boxset if I recall

Metallica's My Friend of Misery and Inamorata

Isn't My Bkyfriend's Badk a sequel to It's My Party and I'll Cry if I Want To? Or the other way around?

Judy is a Punk and Return of Jackie &Judy by the Ramones. Also Havana Affair and This Ain’t Havana by the Ramones.

Not really super well know ones, but:

Marianas Trench - Masterpiece Theatre album has Masterpiece Theatre I, II, and III on it. My favorite album of theirs. The songs from this album actually permeate the rest of their albums after this one.

Sleeping With Sirens - If you were a movie, this would be your soundtrack. A five part musical of sorts that's really well done.

Veruca Salt, in Volcano Girls, they reference Seether.