It's a problem that's been around for quite a while. Like, since the dawn of computers. And it's been solved numerous times in compiler generators, explained in textbooks, etc. Right now most solutions compete on clarity, simplicity and adaptability, not solving the problem itself.

These days the general consensus is to use the Pratt parser, which is somewhat harder to understand, but ends up not too hard to build and integrate into a recursive decent parser, and is supereasy to modify.

Here's one popular explanation:

https://journal.stuffwithstuff.com/2011/03/19/pratt-parsers-...

What I find funny is that Pratt's parser was never really a theoretical result and was never properly covered in popular compiler textbook.