How do you sync iPhone to different computers?

This (iPhone 4) is my first ever smartphone so I'm new to this. My music is on 3-4 computers. I'm trying to add music from computer #2 and I want to do the manual sync up. If I apply it though, it says it will erase all my music on my iPhone since it can only sync up to one iTunes at a time, which just defeats me trying to get all my music. Perhaps I'm missing something basic, but I don't know what it is. I also wanted to sync up ringtones and it says the same thing. Why does it seem so complicated

Also, I have a 2nd generation iPod touch and I don't think I encountered this problem before. Usually when I click on manually moving the songs, it would allow me to.

I think it'd be pretty ridiculous if it won't allow me to sync up all my songs from multiple computers. I don't want to go through the obnoxious route of putting them all onto my hard drive and transferring it to this machine.