using filters on the function from class

If this is your own class that you’re doing this for, and can modify it, then you could pass the instance of the class as an addition argument to the filter callbacks:

class Foo {

   ...constructor, etc. 

   function to_filter() {
      $output="<div class="wrap">";
      $output .= $this->another_function();
      $output .= more html

      return apply_filters( 'to_filter_name', $output, $this );    
      } 
}

function filter_foo( $output, $foo ) {
    $output .= $foo->another_function();

    return $output;
}
add_filter( 'to_filter_name', 'filter_foo', 10, 2 );

The important part is that 2 in the add_filter() call. It passes through both arguments to the callback.