You can only sign in to Google Drive with one personal Google Account (for instance, a Gmail account) at a time. If you're trying to sign in to a school or work account using Google Apps, you can only sign in to Google Drive with one account in a given domain.
To sign in to Google Drive using an additional Google Account, you have three options:
- Share docs and files that you want to access between your Google Accounts so that you can access them with any of your accounts.
- Sign out of all of your accounts, and sign back in using the account you'd like to use for Google Drive. That first account will be the one with Google Drive access. Then, you can continue to use multiple sign-in to use other Google products.
- Use other methods for signing in to multiple Google Accounts.
For Google Apps users: You can sign in to Google Drive with your Google Apps account and with your personal Google Account at the same time. In fact, you can sign in to Google Drive using multiple Google Apps accounts, as long as each one is from a separate Google Apps domain.