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

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]

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

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.

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.

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.

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.

Tool Parabol - Parabola

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).

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

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

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

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

Metallica has the unforgiven, unforgiven 2, and unforgiven 3

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).