Yes, a user can connect to any available options. Right now, that's managed through the SCLogin module. The "My Account" menu in the top right of this site is the SCLogin module. There are options in the module for "Show Connect Account Buttons" which will show any networks the user hasn't already connected to. You can also create a special menu item, like we use in our module, to show the reconnect buttons in the user menu, if you have that feature enabled.
Let me know if that helps answer what you're looking for or if you need more help.
Thanks,
Alex