Some apps take a second account with a label. Gmail does not.
A few connected apps can hold more than one login at once. Official help uses Notion as the example: two workspaces, each with its own label.
If the app supports it, open Connect apps in the sidebar, open that app, and under Accounts choose Add Another Account. Give the extra login a short label, such as work or personal. Choose Authorize and finish signing in. On the phone, open the app from Connect apps and choose Add account.
Then tell the Bot which one to use, by that label. Official help's example is "Use my work Notion." Every Bot on your Grok Bot account can use every connected account, so the label is how you keep them from mixing.
If you do not see Add Another Account, that app connects one account at a time.
Gmail is in the second group. Official help says you cannot keep a personal mailbox and a work mailbox connected to Gmail at the same time. To use a different Gmail mailbox, disconnect the current one and authorize the other. A connected Gmail mailbox is available to every Bot on the account, so disconnect it if a Bot should not use that inbox.
Some setup videos say otherwise. In the walkthrough "Learn 95% of Grok Bot in 32 Minutes," Komputer Mechanic includes adding another account for extra Gmail inboxes. That does not match the current connect-apps help page. Treat Gmail as one mailbox. Use labeled second accounts only where the app actually offers the button.
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