Can multiple vendors provide the same product to a client?

Can multiple vendors provide the same product to a client?

We are a training company so our "product" is the service (for example a workshop) provided by our trainers. The trainers are subcontractors so essentially they are the "vendors" moreso than employees.

One client may order a day of workshops that 3 or 4 vendors will provide. I want to be able to create a report where I can see all the vendors that provided workshops to a given client. Likewise, I want to be able to create a report that shows each vendor and all the clients they have provided workshops to.

Originally I thought I could create the generic product category of "workshop" and link it to each of our 8 vendors, but that doesn't seem to be working. Any ideas?