The preferred method of viewing additional email accounts (such as shared departmental accounts) is to have them delegated to your primary email account, and any documents owned by those shared accounts moved to a Google Shared Drive. In some cases, however, this is not possible - for example, Google Forms that use the Upload feature are not supported in Shared Drive.
Google has added the ability in the latest version of Chrome to have multiple separate profile windows. Such a window works like a Chrome incognito window, but has the persistence of a normal Chrome window - you can close Chrome and re-open it, and it will remember your login. You can repeat this process multiple times and be logged into multiple accounts this way.
Google intended this to be used to keep your various work and personal windows separate from each other, including bookmarks and cookies. Even the Chrome settings are unique to a window.
How to set up an additional account window
In Chrome, click on the profile icon in the Chrome toolbar (not in Google's web page):
Click the "+ Add" button at the bottom:
Chrome will ask you to select a color for the new windows' title bar, so you can easily tell the difference between it and your existing account's window. You can also give this new window profile a name:
Now, you can log into the shared account by going to https://mail.google.com. In addition to the different colors, you can tell which account you are in by hovering over the profile icon in the Chrome toolbar:
Default settings
An important thing to note is that your new window's Chrome settings revert to the default. For instance, if you are used to PDFs downloading when you click on them, they will open in a new tab with this new profile. To change settings for this window, select the three dots next to the profile icon in the Chrome toolbar, and choose Settings.