You can have a single install that uses two different licenses.  You simply activate the Designated Computer license, then go back and open MATLAB, and go to Activate Matlab in the program group.

Choose to activate manually and use the license file and key from the Concurrent Matlab offer on WebStore that you have not already activated - Activate Software to activate the second. 

Your computer will use the local license file from the Designated Computer license by default and, if you try to use a product for which you don't have as part of the Designated Computer license, it will try the concurrent license on the Matlab license server.