I do appreciate that you're not asking how to use fewer symbols, but, ... There are intelligibility problems with too many "variable names with global scope". It's better for things to have "more local scope", and, in particular, with "local" explanation of what the symbols denote. This does also have the incidental benefit of reducing the total number of symbols needed. And... what field(s) is this?

@paulgarrett I definitely agree with you. It may be a bit weird and surprising but this amount of characters hasn't really caused a problem. The submission is chopped up in two parts, and the second part adds a bit more. This paper involves dynamical systems, graph theory, machine learning, multi-agent system, in continuous, discrete and stochastic (markov) settings some analysis on algorithmic complexity on top.

These new characters I am thinking of will mostly be used as placeholder for some variables that are only used locally, say, within an example.

Ah! Well, good luck. I do have an old book ("Classfield Theory" by C. Chevalley, from lectures he gave while visiting Japan in the 1950s) that uses Chinese/Japanese characters to denote objects. It is very hard to read without knowing pronunciations for them. Less severe, but still counter-productive, is the original version of Langlands' book on Eisenstein series (from 1976), in which many key objects are denoted by hand-drawn fraktur letters. :)

Couldn't you "locally" use some characters that do not otherwise appear "nearby"? If people don't know the names or pronunciations of characters that's a non-trivial impediment to their reading your work.

I understand. Originally these characters were simply alphabets, a, b, c, d. Then as we added more material we've realized it clashed with some other stuff. So currently we are using these "var" Greek characters. Which already has the problem you've mentioned. Not many people can recall what varupsilon looks like or know the pronunciation of them when they see them. We've tried using more Latex packages but we have been receiving the "too many symbols" error, which happens when you try to use too many fonts.

Another possibility is to use multi-character names for things... in Latin or Greek alphabets. This can have descriptive/mnemonic advantages, obviously, too.

There's some precedent in the use of the Hebrew Aleph in set theory, but it might be better to use \prime, \tilde, \bar etc. variants or indices instead of introducing unfamiliar symbols.

In some areas of continuum mechanics there were attempts at adopting the Hebrew alphabet years ago. Never really seemed to catch on. For me it was nothing more than unfamiliarity with the names of each symbol and I simply didn’t take the time to learn them.

I think I should repeat a comment I made elsewhere: From the MathSciNet review of the second edition of Bourbaki's set theory (MR0154814) "In the first edition, all alephs except those appearing in exponents were printed upside down; in the new edition the exception has been removed."

If you really want more symbols, try using Roman alphabet letters rotated through 90, 180, or 270 degrees, or reflected left-to-right or top-to-bottom. If you still need more symbols after that, IMO you need to completely rethink how you are presenting your ideas. (That method was used in printed books in the pre-computer era by making special metal type. With computers, implementing it is easy).

$a_1$, $a_2$, $a_3$, ...

A character like 十 is likely to cause some confusion in mathematical writing.

@Winther in that publication they've also exhausted all the natural numbers as indices for every possible character, hence the question.

@Džuris The Natural Numbers are infinite. You cannot use all of them.

I know this is against the spirit of what's been said so far but, you can use the cyrillic alphabet. It would have the added benefit of looking more in place than East Asian scripts which can look quite jarring against Latin and Greek characters

Be sure to use シ, ジ, ツ, ヅ, ッ and 𱁬

Every "legible" character on that page? Are some of them illegible?

See also the use of フ and ヲ as logical constants in the context of linear logic (e.g. p.17).

十 can both be mistaken for + or †, depending on font, lighting and ones eyesight.