No, you can only log in with the email address registered to your profile. You can't register more than one email address to a profile. This is because your email address is attached to your user profile and it's your unique ID to log in.
For companies who use multiple email addresses or aliaises, be sure to confirm with your employees which email is registered to PeopleGoal. If you try to log in with the incorrect email you'll be redirected to the Sign Up page to sign up for a new account or request to join an account. Even if you request to join your Company account with a different email, the system will register you as a new user and you won't be able to access your company profile, because you're adding an email address that has not been set up on the account.