Hi everyone 
I’ve spent most of 2019 with two Asana instances opened on the same browser. Typically I would have 2-3 tabs opened for the Asana Org and one tab for my private Workspace (which I used to organize my wedding)!
Technically speaking, I rarely ran into any issues and being able to have the two instances opened simultaneously made the switch very easy! With that said, you still need to navigate two My Tasks and two Inbox! @Dace if this is a temporary situation I think it is totally manageable to choose one Org and invite the other as Guests!
And if you haven’t yet, you can add your vote to the following threads: