Maximum limit for creating Apple ID from the hardware address of iphone is three , you can't create more Apple ID accounts , however again sign in with your same Apple ID and it's account credentials ( in fact you have signed out the Apple ID ) in the empty fields or sign in with another apple id that was created from another Mac / iPad or different iPhone .
See the article Sign in with your Apple ID - Apple Support
Note : your all devices that are synced with primary Mac are not able to create a new Apple ID as maximum limit of creating Apple ID is over , you need a different Apple ID that is already created apart from your synced devices to get signed in ( your primary Apple ID is say example1@gmail.com ) .