Shortcode for a Shortcode?

So is it possible to create a shortcode that also outputs a shortcode?

I am using the audio player so in my post I enter:
[audio:11071.mp3]

And the player shows, I also have a custom download link shortcode like this:
[media_mp3 m=”11071″]

This second shortcode is needed based on the way I use blog posts. What I’d like to do is combine these, for example, a shortcode that could look like this:

[post_date d=”11071″] = and the out put in the post would result in the same as if I had the first to shortcodes in there:
[audio:11071.mp3]
[media_mp3 m=”11071″]

Not sure if you can have a shortcode trigger another shortcode?! Any ideas?