The first obstacle to watch out for is you can't have multiple tests running in parallel on the same machine at the same time. You'll get conflicts anytime some sort of desktop interaction needs to happen in a test.
Do you have any sort of build infrastructure in place now? One idea would be to split up your tests into multiple Visual Studio test lists, setup multiple test agents, and have your TFS server (assuming you have one) order different test lists to be executed by the different test agents. This would achieve the parallel execution you seek.
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