International Phone Number w/ US Apple ID

Hello,

I'm currently living in Japan, where I purchased an iPhone 5c about three months ago. As such, my phone number is a Japanese one. However, I have a US Apple ID (and have had one for several years now) and it won't let me update my new Japanese phone number. I currently have a family member's phone number listed, but that family member also has an iPhone, so now my phone thinks I'm someone else.

Is there a way to add an international number for a US Apple account?

Thanks for the help!