BuddyPress.org

You can add a tab under ‘settings’ by using the bp_setp_nav hook.
For example:

	bp_core_new_subnav_item( array(
		'name'                    => __( 'New Tab', 'your-domain' ),
		'slug'                    => 'new-tab',
		'parent_url'              => bp_loggedin_user_domain() . 'settings/',
		'parent_slug'             => 'settings',
		'screen_function'         => 'new_tab_function',
		'show_for_displayed_user' => false
	) );

And then use the screen_function to add fields.
But you’ll have to write your own handlers for edit and update of the fields that you add.