Shortcode class output to be returned from a different external class

When creating a shortcode as object, this is the class:

class class_shortcode{
    function __construct(){
        add_shortcode( 'SHORTCODE_NAME', array( $this, 'shortcode_output' ) );  
    }

    function shortcode_output( $atts, $content ) {
        // create some output
        return $output;
    }
}

But there happens to be an external class handling the shortcode output, like this:

class class_shortcode_output{
    function shortcode_output(){
        // create some output
        return $output;
    }
}
class class_shortcode{
    function __construct(){
        $this->display = new class_shortcode_output;
        // Then, the shortcode output will be returned by $this->display->shortcode_output()

        add_shortcode( 'SHORTCODE_NAME', array( $this, 'display', 'shortcode_output' ) );   <---- THIS IS WHERE I AM STUCK
    }
}

So I need the output in within class_shortcode to be handled by $this->display->shortcode_output() from the other class class_shortcode_output. Is it possible?

I am trying these syntaxes:

array( $this, 'display->shortcode_output' )
array( $this, 'display', 'shortcode_output' )
array( $this, array( $this, 'display' ), 'shortcode_output' )

But nothing is working, is it possible to accomplish what I need?