Your Macs Mail app supports multiple accounts with separate inboxes, but you cannot add new accounts directly from the app's settings. To change accounts, you must use the System Settings.
How to add or remove mail accounts in mail
The accounts that Mail uses are directly from the "Internet accounts" section of the system settings. If you want to add a new account, you need to do it there.
To start System Settings, click the Apple menu at the top of the screen and select "System Settings." You can also start it from your Dock or your application folder.
Click "Internet accounts" in the System Settings window.
You will see a list that probably contains your iCloud account. To add a new email message, click the "+" button at the bottom of the list and then click on which mail provider you use. If you do not see your provider, you can manually add your email with "Add another account."
You will be shown a popup asking you to sign in to your email account. Enter your email address and password for the account you want to use and click "Next".
When logged in, you can choose which features you want to link to your email address. If you just want Mail, disable other features like Contacts and Calendar and click "Done."
When it is ready, a new account is displayed in the list. If you open the Mail app settings (Command + Comma) and click on the "Accounts" tab, you will see your account linked in Mail. You can change the settings for this account from here.
To delete an email account, you can either turn off "Enable this account" in the email program settings or delete the account from the "Internet accounts" panel in System Preferences. Click on the account and then click the "-" button at the bottom of the list to remove it from your list of accounts.