Apple Music Payment
I'm trying to add a new card to my apple music billing info, and it's not letting me do that.
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it might be a balance is due or unpaid:
“You can't remove a payment method if you have a balance due. Learn how to pay an unpaid balance or fix payment method issues. After the unpaid balance is paid, you can remove your payment method”.
Read the below link to see if it helps:
If you can't remove your last payment method or use no payment method with your Apple ID
https://support.apple.com/en-ca/HT203905
You could try adding the new one and just leave the old one there for now and remove it later. Make your new one the first choice to be used as follows:
Change the order of your payment methods:
“Tap Edit, then use the Move Order icon 
to rearrange your payment methods. Apple will attempt to charge payment methods in order from top to bottom. You can't change the order in which Apple ID balance is charged”
Change, add, or remove Apple ID payment methods: