Is there a function to add additional options to the Twentyeleven option page?

You can, but currently it’s not easy. You would have to override the existing code, and re-write it to extend it with your additional options.

Start here:

add_action( 'admin_menu', 'twentyeleven_theme_options_add_page' );

You’d need to remove this action (in your Child Theme):

remove_action( 'admin_menu', 'twentyeleven_theme_options_add_page' );

Then, you would need to duplicate the twentyeleven_theme_options_add_page() function in your Child Theme:

function twentyeleven_child_theme_options_add_page() {
    $theme_page = add_theme_page(
        __( 'Theme Options', 'twentyeleven' ), // Name of page
        __( 'Theme Options', 'twentyeleven' ), // Label in menu
        'edit_theme_options',                  // Capability required
        'theme_options',                       // Menu slug, used to uniquely identify the page
        'twentyeleven_child_theme_options_render_page'            // Function that renders the options page
    );

    if ( ! $theme_page )
        return;

    $help = '<p>' . __( 'Some themes provide customization options that are grouped together on a Theme Options screen. If you change themes, options may change or disappear, as they are theme-specific. Your current theme, Twenty Eleven, provides the following Theme Options:', 'twentyeleven' ) . '</p>' .
            '<ol>' .
                '<li>' . __( '<strong>Color Scheme</strong>: You can choose a color palette of "Light" (light background with dark text) or "Dark" (dark background with light text) for your site.', 'twentyeleven' ) . '</li>' .
                '<li>' . __( '<strong>Link Color</strong>: You can choose the color used for text links on your site. You can enter the HTML color or hex code, or you can choose visually by clicking the "Select a Color" button to pick from a color wheel.', 'twentyeleven' ) . '</li>' .
                '<li>' . __( '<strong>Default Layout</strong>: You can choose if you want your site&#8217;s default layout to have a sidebar on the left, the right, or not at all.', 'twentyeleven' ) . '</li>' .
            '</ol>' .
            '<p>' . __( 'Remember to click "Save Changes" to save any changes you have made to the theme options.', 'twentyeleven' ) . '</p>' .
            '<p><strong>' . __( 'For more information:', 'twentyeleven' ) . '</strong></p>' .
            '<p>' . __( '<a href="http://codex.wordpress.org/Appearance_Theme_Options_Screen" target="_blank">Documentation on Theme Options</a>', 'twentyeleven' ) . '</p>' .
            '<p>' . __( '<a href="http://wordpress.org/support/" target="_blank">Support Forums</a>', 'twentyeleven' ) . '</p>';

    add_contextual_help( $theme_page, $help );
}
add_action( 'admin_menu', 'twentyeleven_child_theme_options_add_page' );

Then, you would need to duplicate the theme_options_render_page() function in your Child Theme (e.g. as twentyeleven_child_theme_options_render_page()), adding in your additional Theme options.

Note that, hopefully, this will get much, much easier in a future version of Twenty Eleven. I’m getting ready to submit a patch to convert that theme_options_render_page() function to using add_settings_section() and add_settings_field() calls, rather than hard-coded table markup.