Does a *gapless, read-ahead streaming* mp3 player exist?

I like to stream mp3s from my desktop or archive.org. All the players I've tried operate as follows:

1) Start downloading track from source
2) Start playing when we become confident that the whole track will play uninterrupted
3) When the track is over, repeat 1-3 with the next track

However, I like my music to play gapless, or near-gapless. Are there any music players out there that have an additional step:

2.5) When the current track is done downloading, start downloading the next one

Seems simple enough, no? I believe this would reduce the gap between tracks in most situations when you can download faster than the track can play. As far as I can tell, Windows Media doesn't do this, VLC doesn't do this, Amarok doesn't do this, etc. Windows Media especially has a "Connecting" phase that seems to take awhile by itself.

I just need mp3 support, and I'm interested in what programs offer this for Windows, Mac and Linux.

Thanks=