While in the CCP, you can go through "Your" page to create a CCP case. Additionally, you can search for a business, select their account, and create a case from their "page". When doing this, it would be wonderful if the account information autofill in the client name/ client ID/ and contact fields.
In order to make sure we fully understand the request, when you say "their" page are you referring to the Account Page - Support Cases - View all page where you can select new?