Yes you can sync up to 5 computer iTunes with your iPhone, what I'm not really certain about is if iTunes on computer 2 will agree not erasing your music present in your iPhone before syncing in music. What I have experience was that despite the fact that I have authorized iTunes to recognize your iPhone, it will erase all the music from your iPhone before syncing new musics, unless I'm syncing apps books, pictures and have the music tap uncheck then the music in my iPhone will remain unchanged.