A quick thought exercise on the subject...
The two most popular (and somewhat diverging) ways of leveling characters are milestones and XP.
I assume you know how XP works; it is assigned according to treasure acquired, monsters defeated, etc. If you get enough X, you level up.
Milestones allow you to level up upon the completion for a particular goal: saving a hostage, slaying a particularly important creature, surviving a dungeon, etc.
Most people prefer using one way or the other, but it is easy to see you could combine them: for example, the GM may arbitrarily assign XP rewards for certain goals.
I like using milestones myself, because it allows me for a bit more control over the pacing of a campaign, and also because it requires less bookkeeping.
But I disregard XP entirely: PCs have levels and they level up when appropriate (usually upon finishing a module or two).
In order to do that, I had to balance the classes using feats and a house rules.
This is also the case for my free "OSR Minimalist" game. I always enjoy getting feedback on that!
But what if you WANT to keep distinct XP costs and STILL use milestones to avoid writing down every coin acquired and every monster slain?
There are a few ways to do that.
The simplest way is probably choosing a PC at random to level up, but every PC has the same XP.
If you have 4 PCs, all on 1st level, roll 1d4. It the thief is selected ts to level 2 (1,200 XP), no one else levels up. But if the elf is selected (4,000 XP), everyone else levels up too... and the thief gets to level 3 immediately!
As you can see, some nuance is lost here - some levels will be skipped.
Alternatively, just use 500 XP per milestone until 10.000 XP, then 5.000 until 100.000.
This will give the fighter a level for each 4 milestones, more or less.
After 100.000 XP, you can give 20.000 to 50.000 XP per milestone, depending on how fast you want PCs to level up to "name level" and beyond.
Anyway, this is purely theoretical - I think I'd prefer to use XP or milestones as a primary method and maybe some exceptions.
There is probably a better solution out there... let me know in the comments!
BTW: my latest book, Basic Wilderness Encounters, is now added to my discount bundles. You can buy ALL my books for around 30 bucks!
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