How to resolve 'Sorry, something is wrong' and 'That number is in use' errors when swapping iPhones with Xfinity carrier?

This is an Xfinity issue. Carriers are famous at the blame game. Contact Xfinity CS and elevate this. They need to provision your account for the new phones. Keep in mind that Xfinity is a MVNO (Mobile Virtual Network Operator) who relies on Verizon for their towers. Most lower cost MVNO providers often lack in their technical support. You pay less, you often get less. But they should be able to resolve this. If they can't, then take your business to a better carrier.

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To use two different network providers, your iPhone must be unlocked. Otherwise, both plans must be from the same provider. Contact your network provider for more information. 

If you have an enterprise or corporate data service plan, check with your company administrator to see if they support this feature.