AppleCare+ family sharing with multiple Apple IDs

No. There is no Apple Care One for Families.

Apple Care One is personal. It is not meant for families.

You can only add eligible devices signed in to the same Apple Account.

click here ➡️ Add or remove a device from your AppleCare One plan - Apple Support

Sorry, your post confused me. I didn't see that you later said AppleCare One instead of AppleCare+ which is not the same thing. There is no AppleCare One for families. All items for coverage under AppleOne must be signed in under the same Apple Account.

AppleCare - Apple

Can I add my family’s devices to my AppleCare One plan?

AppleCare One plans can cover devices that are on the same Apple Account as the subscriber.

Apple Support

Yes.