The kind of thing I had in mind is for creating Domain Specific Languages - more toy systems than any new earth-shattering paradigm. It's up to the tinkerer. Like, maybe someone wants to add coroutines to the language, for example.

I had one idea in that I'd like to add a nicer way of expressing the parsing of data.

Maybe a Cobol, but nicer. Or a Snobol, but in a more general-purpose language.

Another idea is in the realm of microcontrollers. It could write start-up code for peripherals, and ensure its usage doesn't conflict. I'm not a Rust programmer, but I am aware that it is the kind of problem it addresses.

BUT, the thing about compilers is that a function call is just a function call, it has no idea of intent. By extending the language, you can give the compiler that intent. So certain functions can have compile-time semantics as well as run-time semantics. You could probably achieve the same kind of thing with Lisp.

Anything where one feels the need/desire to extend syntax, basically.