Shortcodes into shortcode

I need an information if possible, because I don’t find anything arount about this situation.

I would like to run some shortcodes (or just one) called from another shortcode.

To do this I put this code under my child theme’s functions.php:

add_shortcode('format', 'shortcode_block_format');
function shortcode_block_format ( $atts ) {

switch( $atts['which'] ) {
case '1' : return do_shortcode('[my-old-shorcode]'); break;
case '2' : etc etc
}
}

but when I write [format which =”1″] in the editor, and then I save the post, the result is just this written on the frontend page:

[my-old-shorcode]

So the new shortcode [format which =”1″] works because it makes the old shortcode [my-old-shorcode], but [my-old-shorcode] is no longer interpreted by wp, who “sees” it just like any other text.

The question is: there is a way to RUN a shortcode called from another one?

Thank you!!