How to run a build server task under a specific user account?

I require my VSTS build server, or more accurately my build agent, to execute a task under a specific user account. Example:

One of my build steps tests the UI of an application. It requires to be logged in under a different account to be able to execute tests correctly. I cannot find anything in VSTS that allows me to configure that.

My current workaround is to run my tests in a different thread, started via a PowerShell command; however, this solution feels dirty, is fairly complicated, has limited live reporting and costs work to re-integrate the test results.

Is there any better way, maybe one that work straight out of the box via VSTS?

Note: Changing the build agent to run under a different account doesn't work because I need to run tests under multiple accounts long-term to test various authentication features.