This is sort of an unusual request; it's not all that normal for someone to want to hear the same songs over and over again but in a different order.
How long would you want this to continue? Is this for a specific purpose, or is this just how you like to listen to music?
If you were to say, for example, that you wanted to hear music for 3 hours or 4 hours like this, then you can definitely do this. Here's one way:
1. Add your songs to a playlist.
2. Add the same songs to the playlist again.
3. Look at the total time. Do you have enough time yet? If not, go to step 2.
4. When you have enough total time, Press Reshuffle to randomize the entire list.
5. Add it to Playing Now and play it.
You can make arbitrarily long playlists. You could put 10,000 songs in a playlist if you wanted and randomize the whole thing. 10,000 songs would be about 3 weeks of continuous play, assuming roughly 3 minutes per song. This is kind of a silly example, but I think you get the point. Just make the playlist longer for longer play times.
Brian.