You should add extra domain name as addon domain name in cPanel to host more than one domain name under new account. But web hosting companies may put limitation on number of addon domains allowed. You can see addon domains limit in cpanel left side.

Yes, you can use multiple domains to open/ host same site using “parked domain name” feature. Add extra domain name as parked domain name in cPanel of your account.
Remember all parked domain names should have same nameserver address as used by main domain name of your account.