Thanks to Phoneable, a free Windows application you can now sync multiple iTunes libraries
Initially your iPhone is synced with the first computer you use it with. When you plug it into a second computer you can’t sync or manage the music on the phone. PhoneAble allows you to manage your music manually on the 2nd computer, which is different to syncing your music. You can still only sync music on the first computer.
1) On the second computer, plug your iPhone in, and back it up by right clicking on the device in iTunes and selecting backup.
2) Now close iTunes and run PhoneAble, run through the steps.
3) Open iTunes again, click on the phone in the devices section, then on the summary tab there is an option “Manually manage music and videos”, make sure that is on and Apply the change. Now try and drop some music files on the iPhone device, it should now allow you to copy music to your own phone.