If you manage multiple @appstate Gmail accounts, there are two methods to access those accounts in the same browser: Managing People in Google Chrome and Account Delegation
Manage People
In Chrome, click your profile icon in the top right corner of your browser.
In the pop-up context menu, click add to add another profile or click on another user under “other profiles” to switch to that user (If you click to add another account you will be prompted to log into the @appstate account that you wish to add. You can repeat this process for each @appstate account that you manage.
Account Delegation
Reference this tutorial to manage users using account Delegation: Setting up Mail Delegation in Gmail