You can do this by having multiple installs of Chrome. You could have stable chrome, along with the beta, dev, and canary versions installed. Same can be said for firefox beta, dev, and nightly. Sessions won't be shared or conflict with each other.
If you only need 2 instances open at a time, it's simpler to just use Incognito Mode for the second one.
I had about 7 that I regularly logged into (including sandboxes), but rarely needed to log into more than 2 at the same time. The long sessions I logged into normally, the shorter sessions I used incognito mode. If I was hopping between sessions I also often used incognito mode, rather than logging out each time, because you can just close your incognito window(s) to clear the login.
The other part that made it manageable was having a series of bookmarks with the Company Name prefilled, using the format: https://login.eloqua.com/?SiteName=123 Only needing to type username & password makes it rather quicker to switch!
I usually have 1 normal Chrome, one incognito mode and the same thing in firefox (one normal and one incognito). So I can multitask but beware not to mess up sessions and actually when I do that I realise that I am not as efficient as when I focus on one client at a time.
Good luck :-)