User testing of multi dimensional information architecture

i'm working on a project where I have to test an information architecture. This kind of IA is multidimensional. So you can access to the same content through several path. Each content is tagged with some metadata (i.e. users type, service type, duration). The site has two main entry points (browse by users type and browse by theme). In addition it has a search bar and a help tool to find a specific service. This tool works asking users to choose one or more user type to whom the service is referring to and one or more theme theme to narrow the search results.

How would you test the information architecture of this site? I was thinking about a card sorting exercise, where each dimension (user type, theme, duration, service type) is a category and the content type are the cards that need to be grouped under one or more categories. Categories can overlapping (like venn diagramm) because one content can refers to two dimensions.

Do you have suggestion? What would you do?

Thank you so much