“Implemented in” is the key. If you want, say, a C compiler written in Lisp, you end up writing a compiler. If you want a Haskell compiler written in Lisp, you write another compiler.
If you want Avail to include all of C, you define C language capability in an Avail module and subtract the rest. Then your C program is also an Avail program, so you have the same tool chain you had with core Avail (still lacking, but getting there), you have dynamic optimizing compilation to JVM (and eventually native, perhaps), and you have a program that not only interoperates with programs written in other dialects, but allows direct connection between them. Like if you want Avail exceptions with your C code, you import exceptions and just use them. You don’t build them over and over again for each language. And if you want to support closures in your C, you’d probably just remove the limitation that treated the closures of Avail as contextless C functions. Similarly for backtracking, universal serialization, and sensible module dependencies (maybe call it #import, versus the horrible textual #include mess of C).
And finally, if you want your existing vanilla C code to be able to call “out” efficiently to some FORTRAN or Python code, you no longer have an impedance mismatch. Define those dialects as Avail, and you’ll have real garbage collection, multiplexed lightweight threads (fibers), dynamic optimization, and objects and functions that are reasonably compatible between these dialects.