I have a USA amazon account and a Japan amazon account. They are completely separate. So yes, it's easy to sign up for Prime multiple times if you use multiple accounts.
https://us.amazon.com/gp/help/customer/display.html?nodeId=2... Change your Amazon Account Country
Important: If you create a new Amazon account instead of transferring the existing account, purchases won't be shared between the accounts. You’ll have separate login credentials for each account.