It works just like you suggest:
You sign up, and get a hosting plan and a user account to access it. You can in fact get a user account (a WebID) without even having a hosting plan, so maybe you already have an account (without a hosting plan).
Once you have your Code Monster hosting plan and your user account, you can register new or transfer existing domains to it. They will all be listed as separate domains inside the control panel of your user account. This way, you can manage all domains with just one user account.
If you want to allow certain other users to access and/or maintain certain domains inside your plan, you can do this as well. Create a user account for each person, or have them do this themselves.
Create new user accounts here: https://panel.dreamhost.com/login/new.cgi or, if you want to be nice, use this link instead. It will make no difference to you but I may earn some referral points.
Once the other users have their WebIDs, you can grant them access to your domains. You can choose which of your domains they can access and what permissions they get, so you can allow them access to precisely those things that you want to share, and still keep the rest to yourself.
Grant other users access using the page: https://panel.dreamhost.com/index.cgi?tree=home.access&
(Disclaimer: I’m just a user and I’m not on the code monster plan. My advice is based on what I know as a regular customer with two domains in one plan.)