How to add “supports” parameter for a Custom Post Type?

Yes, there’s a function called add_post_type_support

Hook into init — late, after the post types have been created — and add support.

Adding support for excerpts to pages for instance:

<?php
add_action('init', 'wpse70000_add_excerpt', 100);
function wpse70000_add_excerpt()
{
    add_post_type_support('page', 'excerpt');
}