this is a good article that define how to do network calls from front . IF you check each implementation it mention browser support
You could use Pabot: A parallel executor for Robot Framework tests.
From their GitHub page. You can find more advanced use-cases and documentations here.
Run same tests with two different configurations.
pabot --argumentfile1 first.args --argumentfile2 second.args [path to tests]
I am not very familiar with RIDE, but I think you can configure Pabot as an ...