Assigning one test case to multiple owners

I am in a project situation where there may be a necessity of having the same test case assigned to different Owners.

At the moment, I had thought of assigning each test case to an owner and later when the user finishes testing, have the same test case assigned to a different owner. Every users' test case execution will then be saved as a separate Test Run. Is this the right approach? The drawback of this approach would be the users would need to wait until the first execution has completed and cant run this in parallel. In contradiction, I can setup this as different test cases and assign any owner against it, but this would lead to duplication of test cases as test steps would be the same each time.

Can anyone suggest a better way of playing this?

Thanks,

Praveen