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Have you tried Rampage Knights? Its not quite in the same style as an old Capcom beatemups, but its an exceptional 2d re-imagining of the genre with a lot of replayability due to unlockable classes, challenge modes, difficulties, different level arrangements, trinkets, weapons, items, potions, magic, and other powerups each time you play. And the 2 person online multiplayer is excellent too.

https://store.steampowered.com/app/314410/Rampage_Knights/

https://store.steampowered.com/app/71164/Streets_of_Rage/
https://store.steampowered.com/app/71165/Streets_of_Rage_2/
https://store.steampowered.com/app/211206/Streets_of_Rage_3/
https://store.steampowered.com/app/34276/Golden_Axe/
https://store.steampowered.com/app/71112/Golden_Axe_II/
https://store.steampowered.com/app/211202/Golden_Axe_III/
https://store.steampowered.com/app/34315/Alien_Storm/

Simply look em up on youtube or so and decide yourself which fits to your taste.
Streets of Rage seems fitting for me

Funny thing, but those who play beat 'em ups in a more serious way (sometimes for a living, kind of), consider it one of the mid to low tier Capcom beat 'em ups. Titles like Knights of the Round, Armoured Warriors, Battle Circuit, the D&D games, even Final Fight and Aliens vs. Predator tends to be more favoured. Cadillacs is like the Punisher game, people are more likely to know about it, it was always more "mainstream". (Plus both are very loosely based on comics.)

Please try this modern take on the genre: https://store.steampowered.com/app/674520/FightN_Rage/
Made by a single dev, adding content from time to time. It's an awesome game to play alone, co-op (1-3) or with CPU players!

Cadillacs & Dinosaurs really isn't the best Capcom beat'em up. It's about on par with Final Fight, but Final Fight gets a pass for being the first Capcom game in that style. (Technos' Renegade/Kunio-Kun series probably being the first, and Double Dragon really starting the genre)

If you stick with Capcom, try the D&D games (available on PC), Punisher or Aliens vs. Predator (need to emulate those, they never saw rereleases because of licensing etc.), or Armored Warriors.
AvP is pretty straight-forward but faster-paced gameplay wise. The othersall have interesting extra gimmicks attached.

River City Ransom Underground is also worth checking out. Art style may be cartoony, gameplay is not. It's also a distant sequel to the aforementioned Kunio-kun.

The punisher arcade is the most similar to Cadillacs & Dinosaurs, i also recomend TnmT arcade, Tnmt turtles in time arcade, golden axe 1(genesis version has extra stages) and street of rage series.

Grief Sindrome
SENGOKU 3 (aka Sengoku 2001).
Shadows over Mystara: the best beat em up ever made.

Streets of Rage series
Golden Axe series
Double Dragon series
Final Fight
The Punisher
Knights of the Round
Warriors of Fate
The Simpsons Arcade Game
X-Men: Mutant Apocalypse
Hook

Violent Storm
https://steamcommunity.com/sharedfiles/filedetails/?id=773468275

I'm surprised someone else knows about that game. No one is talking about it. It's a shame.

Undercover Cops
Shadow Warriors (aka Ninja Gaiden)
Shadow Force
Legionnaire
Vendetta
Night Slashers

Wow.. that brings back memories.
One of the best games that I have ever played from childhood.

aces wild (it doesn't have the same up/down control but it's a great game.)
castle crasher
Dungeons & Dragons: Chronicles of Mystara
Street of rage 1 to 3