It’s better to offer multiple social profiles login option in Magento. Also offer Twitter Login option along with Facebook & Google +. I would suggest to use Social Login extension by FME which supports multiple social profiles like Google +, Facebook, Twitter & Yahoo.
Customers can also login with existing accounts & recover lost passwords using the same Magneto login popup window.
Some of the key features are:
Simplify Login/registration process
Automatically updates user profile
Allow manual login/registration
Multi-store & Multi-language
100% Open source
Demo: https://www.fmeaddons.com/magento/social-facebook-twitter-login-extension.html