I use the evil Chrome browser from Google, and I'm stuck in it for this exact reason. As a freelancer who works with many clients and all their accounts, it's important for me not to have to log in and log out of everything all the time. Not to mention I wouldn't be able to keep my finger on the pulse of my own networks.

Chrome has a feature called Chrome Profiles that allows you to create separate instances of Chrome where you can log in to different accounts. When I'm doing client work, I almost always have that client's Chrome Profile open in addition to my own.

Here's the info on how it works - https://support.google.com/chrome/answer/2364824?co=GENIE.Platform%3DDesktop&hl=en

As soon as another browser gets this, I'm out of Chrome.