Adding Fields to the Registration Page

I'm trying to add registration fields to the account/register page and I eventually would like to access these fields from a modified profile plugin and other plugins. I see how I can override the action and view associated with user registration but the action calls a function register_user() to actually complete the registration. It looks like this function is defined in engine/lib/users.php. I'm not sure if I should be editing users.php. What is the cleanest, most logical way for me to do this?