Is it possible to manipulate the list of page templates?

The workhorse is WP_Theme::get_page_templates() (wrapped by the helper function get_page_templates()). If you check out the source, you’ll see:

/**
 * Filter list of page templates for a theme.
 *
 * @since 3.9.0
 * @since 4.4.0 Converted to allow complete control over the `$page_templates` array.
 *
 * @param array        $page_templates Array of page templates. Keys are filenames,
 *                                     values are translated names.
 * @param WP_Theme     $this           The theme object.
 * @param WP_Post|null $post           The post being edited, provided for context, or null.
 */
return (array) apply_filters( 'theme_page_templates', $page_templates, $this, $post );

Example:

function wpse_226324_page_templates( $templates ) {
    // Remove tpl-home.php template
    unset( $templates['tpl-home.php'] );

    // Add custom template
    $templates['tpl-custom.php'] = 'Custom Template';

    return $templates;
}

add_filter( 'theme_page_templates', 'wpse_226324_page_templates' );

See also theme_page_templates code reference.