As mentioned below, you can order or deploy more environments. I wonder what is your definition of parallel testing. If this is about two users testing the same application, you don't need another UAT. If the application version and/or customizations are different, then indeed you would need more than one environment.
The answer is yes, you can have two UAT environments for testing. As Anthony mentioned, you can order for an additional Tier 2 or Tier 3 environment for testing. You can later call the 2nd testing environment as a Pre-Production environment or UAT environment and the existing Tier 2 environment as a Test environment/UAT 1 environment.
Both these environments can have the same source code with same or different data.
Hope this helps. Happy to answer questions, if any.
Sure, order an addition Microsoft hosted Add-On environment (Tier 2+) via your CSP deploy it on your project, and deploy the same Data and Packages to both environments.
Transactional data wont be aligned, but you can test the same release in 2 environments and align the base data before UAT.
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