At work, I almost always have 1) RainyMood playing as white noise, and sometimes 2) some music/news playing on top of that.

Here is how I setup my audio players:

one local player, one web-based player

In this case, I play the RainyMood.mp3 in any local audio player. And then I play the music/news within the browser, by loading this page.

both local players

To play both white noise AND the music/news in local players, I use this in Ubuntu 12.04: