You can open your RSI event and InterStar ICP in 2 different windows of the Chrome browser [not tabs]. Then position the windows on your screen in such a way that each window occupies 1/2 of your screen.
You should be able to control microphones in those windows completely independently. [We did not test every microphone but it works in our test].
Or you can use software for your main RSI event on one half of the screen, and InterStar ICP in the Chrome browser on the other half of your screen.
That way you will not have to use 2 devices unless you want to.