I want to have 2 Testsessions started, both TestSessions should be Assigned to me. I can just Start one at the same time
In what? JIRA doesn't have "test sessions" - you'll need to explain what these are, and/or what addons or other systems you are using for them.
I am using the Addon JIRA Capture
You can't - the point of a session is that's what you need to do at the time. So a user can only have one session running at a time.
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