You have to combine all the songs onto one computer and then load them to the iPod. I believe the record companies would describe what you want to do as illegal.
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One computer will sync with many iPods, but one iPod will sync with only one computer. This is to prevent people from doing what your friend wants you to do (which Onhwy61 correctly describes as illegal), but still allow you to buy iPods for your whole family and download music to them all from your home computer.