Can I Specify Parameter Type as One of Many Types Instead of Any Type in TypeScript?

Typescript 1.4 introduced Union Types so the answer now is yes, you can.

function myFunc(param: string[] | boolean[] | number[]): void;

Using other type than the ones specified will trigger a compile-time error.

If you want an array of multiple specific types, you can use Union Types for that as well:

function myFunc(param: (string|boolean|number)[]): void;

Note that this is different from what OP asked for. These two examples have different meanings.