How do you update a pointer that has to go through 3 functions?

Let's say I have a pointer inside function1, I need to pass it to function2, and function2 needs to pass it to function3, function3 needs to update that pointer. How do you correctly do this?

Do you use triple stars? If so, what's the correct way to pass the pointer inside function2?

function1(void){
    char *pointer;
    function2(&pointer)
}

function2(char **pointer){
      function3(&(*pointer));
}

function3(char ***pointer)}
    /*update pointer*/
}

My question is specifically about this situation only (3 functions), I don't want to remove function2, even if it does nothing.