I need to set up another iphone

You can back up two iPhone to the same iCloud account. When you say "independently" it isn't clear if you mean just as a second phone number or if you mean that you don't want to share any information such as the Contact list. Either way, you can control how much is shared between the phones but if there is data such as Contacts or Photos that you don't want shared between the phones, you would only be able to sync that data from one of the phones to iCloud. Note that syncing data between the devices and to iCloud is different than doing a backup to iCloud.