Tracking time against Clients and Projects

We have a number of products (projects) and each product is subscribed to by many clients. A particular client may have also purchased a number of our products. We want to use MyIntervals for development lifecycle but also for tracking amount of support given to clients. Therefore ideal scenario for us is to be able to create an additional Work Type of "Client Support" and have support resources log their time against BOTH Client AND Project. This will then give us very powerful reporting and analysis capabilities, such as:

- Have a cross chart of Project vs Client filtered for: Work Type of "Client Support" for a specific time period.

My current understanding of the MyIntervals concepts are that a project can only belong to one client. Furthermore when adding time, the client's name only appears when there is at least a project owned by that client. This is restricting. Ideally we need the list of Clients and Projects to be independent but more loosely linked to each other.

Could anyone confirm whether my understanding is correct and advise how we can set-up MyIntervals to accommodate our requirement?