Is it possible to set up a second iCloud email account on my iPhone 15 Plus?

Yes. But the real question is, what exactly is the purpose if this.

If you just want a secondary email address, you can create an Alias on your current iCloud account and any email sent to the alias will arrive at your regular iCloud email inbox.

click here ➜ Add and manage email aliases for iCloud Mail on iCloud.com - Apple Support

If you want an entirely independent iCloud email account you can add one in Settings ➜ Mail ➜ Accounts ➜ Add Account. This will provide an additional email account, and iCloud account with storage and all other iCloud features. Note however, that storage cannot be merged, and you will only have access to email on the iPhone.

If you want to use the account for purchases in the iTunes and App Stores, you will need to sign out of the existing one and log in with the new one and again, purchases cannot be merged, but they can be shared.

What are you trying to accomplish exactly?

wjmhk wrote:

set up a second Apple ID for use in a different country in order to download local apps.

No, you can only have 1 Apple ID signed in at a time on the device for iTunes and App Store, and if you sign out, and then sign in a different Apple ID and download an app you will lock the other one out for 90 days.

Coupled how? What exactly is this coupling doing?

If he has his own iCloud account, then it should already be separate, it may be part of a Family Sharing group you are the organizer of, but that does not mean it’s coupled or connected in any way to your account directly.

What exactly are you trying to accomplish by separating them? What can’t he do now? Explain the specific issue and what the outcome should be, and someone may be able to advise.

Rarely is creating a completely new account the solution.

set up a second Apple ID for use in a different country in order to download local apps.

My son's icloud email is coupled to my iphone account and I want to separate it. Apple support told me to create a new icloud email then I could remove his from my account. Does that sound correct?