How do I add another Apple ID to my device

Except for a few very specific purposes you cannot. Apple's mobile devices are designed for single user funtionality only.

There are several likely places where you can use a different Apple ID:

1. In Mail if you want to use a different iCloud account. Settings -> mail -> accounts -> add account -> iCloud

2. Messages and Facetime. Sign into a different Apple ID for these services in Settings. Note this has to be the same ID for both. Go to Settings > Messages > Send & Receive, and make sure both your telephone number and Apple ID are input there and both show a checkmark. If you need more help, check out this link: Add or remove your phone number in Messages or FaceTime - Apple Support .

3. In If you subscribe to Apple One and use a different Apple ID for iCloud - Apple Support Apple makes sideways reference to using a different Apple ID for media subscriptions and purchases but doesn't describe how to do this.

In iOS/iPadOS: Go to Settings > [your Apple ID] > Media & Purchases. Sign out of your current ID and sign in with a different one.

In Ventura: First, quit Settings. Then, in App Store, choose “Sign Out” in the Store menu, then click on the “sign in” button that appears in the main window. You can then sign into the other account. ( https://discussions.apple.com/thread/254568066?answerId=258576965022#258576965022 )

4. Use a different Apple ID to share purchases with Family Sharing

Use a different Apple ID to share purchases with Family Sharing - Apple Support

For what purpose exactly?

You can have different Apple IDs for each of the different services that use one: FaceTime, Messages, iCloud and iTunes & App Stores, but you cannot have multiple Apple IDs for the same service. Only one Apple ID can be logged in to each service at any one time.

What exactly are you attempting to accomplish?