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You can definitely do both, though it is possible that you can't use the same LiveID/MOS ID for both.
The trial of Windows Intune operates through the consumer and partner portals. Below is a link to the consumer try/buy page. If you get redirected to an Office365 login page, make sure you are logged out of all services that require a Windows LiveID (or MOS ID) and close ALL browser windows, and try again