You can run selenium-server-autonomously several times with different parameters. However, seeing that you are experiencing unexpected behavior, we can conclude that such use is not supported, since there is no documentation that can be found. To find the root cause of your problem, you need to perform additional debugging.
A selenium stand-alone server comes bundled with a grid server. The grid server was designed (exactly the way you want it) to run and manage multiple tests. This allows you to run multiple tests in parallel, manage browser settings and track test results.
Http://docs.seleniumhq.org has a guide to setting up a Grid server.
It is unknown and unlikely that you can run the Selenium IDE HTML Suite -htmlSuite directly using the Grid server. There is no documentation on this document. However, you can export your existing Selenium IDE HTML Suite to WebDriver-compatible code.
Of course, you can always choose to run tests on several virtual machines, this route also solves the problem due to the inability to run multiple instances.
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