When Google sends you to Microsoft's login system, you should be able to choose a Microsoft account to access Google with.
Google does not send the user information you entered to Microsoft! It only identifies that the user is a valid Geneseo Google user. You will log in to Google as whatever user Microsoft reports back to Google.
Google has mechanisms for granting access to another Geneseo user's Gmail and Calendar account that they call Account Delegation. We recommend this method because it avoids having to share a password and managing multiple Microsoft account login sessions.
If you share such a calendar with the Make changes & manage sharing permission, the grantee will see the shared calendar under "My calendars" in Google Calendar, and will be able to interact with events on that calendar as the owner of the shared calendar.
Account Delegation only works with other geneseo.edu accounts and can take up to 30 minutes to show up under the grantee account.
Chrome, Firefox, and Microsoft Edge let you configure separate, persistent containers for your session information called Browser Profiles. This feature generally assigns a profile to each browser window, allowing you to to be signed in to different accounts in different profile windows. Firefox is more complicated - see the link below for more details.
When adding an account to iOS, you are prompted to sign in to your existing account automatically. You can sign into a second account by clicking the back arrow then selecting sign into another account.