I think you should make a new team and put the project in that new team. Either share the project with your customer, or the team (and the project), depending (see more below).
I think of structure in Asana in this way:
The thing we first think of always in Asana is: “I need to make a new project for such-and-such…”
Whenever I hear this, I always pause and ask, for which team/workgroup is this project needed. That’s because, in Asana, you must put a project in a team (assuming you’re structured as an Organization which is preferred; a Workspace setup has no teams so then you need to consider multiple Workspaces in that case.)
This is a good time to get your teams structured correctly and not have it be haphazard, so it’s worth some thought in order to be well set up well for the future. Sometimes you have teams that parallel your firm’s organizational structure, but often too there are transient teams that parallel workgroups that form around one-time initiatives or projects.
So if you step back and think about the structure of your workgroup/teams, and even create those in Asana with no people or projects within them yet, it will help you visualize a coherent structure into which new projects will automatically find a logical home. That will help you decide where to put your project, and whether your customer would be a member of the team, the project, or both (sensible structures could be created in any of these manners).
Larry Berger
Asana2Go & Asana Certified Pro consultant at Trilogi