For my own gmail account, I have multiple email addresses associated with it. For example, I have an email address from my university that is associated with my gmail, and I ca
Your description is a little vague. Are you talking about send-as alias accounts or alternate email accounts?
Send-as Alias
Either way, you can interact with the send-as accounts here: Manage Send-as Alias
Alternate Emails via Admin SDK
Federated Login
Also, I'm not exactly sure how you are trying to incorporate this functionality into your site but another area I recommend checking out is Federated Login for Google Account Users. This might also provide you with the functionality you seek.
Using federated login (also known as federated identity), your website or application can allow visitors to sign in using their Google user accounts. Federated login frees users from having to set up separate login accounts for different websites, and frees you from the task of implementing login authentication measures.