extern "C" may be the only required one:
Every implementation shall provide for linkage to functions written in the C programming language, "C", and linkage to C++ functions, "C++".
However others can exist as per this quote:
The string-literal indicates the required language linkage. This International Standard specifies the semantics for the string-literals "C" and "C++". Use of a string-literal other than "C" or "C++" is conditionally- supported, with implementation-defined semantics. [ Note: Therefore, a linkage-specification with a string- literal that is unknown to the implementation requires a diagnostic. — end note ] [ Note: It is recommended that the spelling of the string-literal be taken from the document defining that language. For example, Ada (not ADA) and Fortran or FORTRAN, depending on the vintage. — end note ]