I was recommended to just go from a beginner distro to an expert one. However, and don't think I want to do that.

I've worked with Ubuntu, Mint, and a very small bit with a beginner's RedHat-based distro that I don't remember the name of

So I want to try out an intermediate-level distro. Does anyone have any suggestions?

Not sure if it matters, but I'm in computer science (so far have only taken classes on C++, very basic algorithms and basic digital systems like logic chips).

Void https://www.voidlinux.eu/

maybe arch too.

Apart from literally building thw whole thing from src eg LFS, there's no real difference - it's all about how you use it.
To become more 'advanced' start trying to achieve stuff as much as possible at the cli, avoid GUI.
Start adding services like eg apache, SQL etc and see if you can set them up correctly.
Add VMs so you can do local networking stuff eg mail, ldap nfs etc.

HTH

If you were comfortable with Ubuntu, you might consider Debian, which is the basis for Ubuntu and many other distributions and is more fundamental. I don't consider myself an expert in operating systems, but I am able to handle Debian and resolve most problems myself or by finding known solutions here at LQ or elsewhere on the net. Debian is stable and handles old hardware as well as new. It is my primary working OS.

Slackware. Though I would not tag it as "intermediate."
It's more hands-on than Debian, but not nearly so DIY as Arch or Gentoo.

When you do a full Slackware install, you must do your own partitioning and, when the software install is complete there are a few steps to finish configuratioin, but, when you are done, you have a fully functional install with a choice of DEs/WMs. And it's rock-solid stable.

I started with Slackware and I'm glad I did; once you understand Slackware, no other distro can intimidate you, because Slackware teaches you how to figure stuff out.

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I'd agree, slack is a bit more advanced than others.

I agree with flshope's suggestion: Debian.

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And Slackware gently teaches you because all you need to do is read the documentation.

AntiX, of course - make it as easy or as hard as you want - re build your own distro, live boot, persistence boot, or install it, how far do you want to go - or you can just install & use it.
http://antix.mepis.org/index.php?title=Main_Page

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i like the notion of intermediate.
i always used to say that's why i liked and used first crunchbang, then bunsenlabs - usable out of the box, but designed for someone who prefers to edit plain text files instead of getting a GUI for everything.

I'm not sure that I understand such labels as "beginner" and "advanced". Linux Torvalds is presumably an advanced user, but I know he likes Ubuntu and "couldn't see the point" of Gentoo. For me, the question is whether the distro does the job without making a fuss. Yes, Slackware is not difficult to install (I've done it), but I've never fancied all the messing about involved in getting a decent set of software.

If you really want to know how things work, you can investigate any distro, but make sure that what you learn is transferable. There's not much point in learning Lilo and System V init when everyone else is using Grub and systemd! From the point of view of a programmer or systems administrator, most of the other differences are just cosmetic.

PS If you are aiming at a computing career, just get Debian or CentOS, or both!

Thanks for all the suggestions

So far I'm thinking slackware. I like the idea of something with good documentation (although I don't know at all if this is typical for most distros or not)

Slackware would be my recommendation. Easy to install, rock solid, and good documentation. For Linux distros, documentation is pretty hit-and-miss. Slackware, Gentoo, and Arch seem to have the best documentation. The BSDs tend to have better documentation than Linux, particularly OpenBSD.

I actually spent this past weekend successfully installing Gentoo, after three previous unsuccessful attempts. It was instructive, and dare I say, fun, but in the end, I had to ask myself whether it was really worth it. Speed, stability, and resource usage were on par with Slackware on the same hardware, but Slackware takes about 1/16 as long. Granted, I'm highly accustomed to installing Slackware, and new at Gentoo, but still.

I reckon most of the mainstream distros have a lot of docs these days.
Have a look at www.linuxtopia.org

Well, that's Slackware off the list then!