Operators not only have precedence, but also associativity. Building a parser that works for arbitrary precedence and associativity is a standard school project that takes only a few lines more code than a parser that deals with operators with a single precedence level.

Here is an example in Haskell for operator parsing that uses nothing no more than the standard library: https://hackage-content.haskell.org/package/parser-combinato... Excluding comments it’s less than 50 lines of code, and it handles arbitrary precedence, prefix and postfix, ternary operators, infix operators with all three kinds of associativity.