My iPhone can’t create a new Apple ID

If you have created the maximum number free accounts on your phone, you can create a new one on another device and use it by signing in via a browser.

See How to create a new Apple ID https://support.apple.com/en-us/HT204316  and

See the data implications below.

Some of these things may apply even though not changing an Apple ID: What to do after you change your Apple ID or password https://support.apple.com/en-us/HT204071

 Keep in mind that some things available under a first Apple ID will not be available under a new Apple ID. For example, you won’t be able to transfer anything purchased from the App and iTunes Stores to the new ID. And, there are other issues to be addressed.

And see what Eric Root says on this matter here  https://discussions.apple.com/thread/251483565 and

what Winston Churchill says about it here: https://discussions.apple.com/thread/7452747

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But, despite any other data loss you can set up family sharing between the IDs to share purchases made with them. See:

Family Sharing  https://support.apple.com/en-us/HT201060

Set up Family Sharing https://support.apple.com/en-us/HT201088

If your apps device has reached its lifetime limit of creating 3 iCloud accounts, then you will need to use another Apple device to create an AppleID and a new iCloud account with that AppleID.

The limit of 3 free accounts only applies to the creation of new AppleIDs/iCloud accounts on a device. There is no limit to how many existing accounts can be used with a device.

But you will need access to another Apple device to make a new AppleID and a new iCloud account with that AppleID before you can use it on that iPhone.