Q: How do I add ringtones from my iPhone to iTunes on a new computer?

I have an iPhone 5s with personalized ring tones on it. I recently got a new computer, and I want to add a new ringtone to my iPhone from that computer. However, when I try to sync the phone, it says that I will lose all my old ringtones. I've backed up my iPhone. How can I add new ringtones and still keep the old ones? Is there a way to add the ringtones from my iPhone to iTunes?

Thanks!