There’re however some limitations here. One, if you sign-out of one Google Account, you will automatically get logged out from all your other Gmail / Google Accounts as well. Second, if you are launching a new browser session, you’ll have to log in to all your Gmail accounts separately because you can switch from one account to another.
Alternate Approach - Sign-in once for all your Gmail Accounts
Let’s say you have three Gmail accounts – one is your primary account that you need to check throughout the day while the other two email accounts aren’t that important.
Wouldn’t it be nice if you could just log into your main Gmail account and automatically get signed into all your other Gmail accounts as well but without having to type the login credentials of any of those accounts? The trick is really simple.
Gmail offers a useful feature called Email Delegation where you can share your inbox with other people (say your spouse) but without revealing your password. Once you delegate your Gmail account to someone, they get instant read-write access to your mailbox and they get signed in to your Gmail account as soon as they sign in to their own Google account.
If you apply the Email Delegation facility to your own Gmail accounts, you can check all your mailboxes by simply logging into your primary Gmail account. Here’s how:
Sign-in to one of your secondary Gmail accounts and go to Mail Settings –> Accounts –> Grant Access to your account (screenshot). Choose “Add another Account” and specify your primary Gmail email address here. You’ll now get a confirmation email (screenshot) in your primary mailbox. Accept the request and repeat these steps for all your other Gmail accounts. That’s it. Once you sign-in to your main Gmail account, you also check all your secondary email accounts by choosing the “Switch Account” option in the upper left corner of your Gmail window. There’s absolutely no need to manually sign in to any of the other email accounts.
Mail settings > accounts> grant acess 
