2 Navigations – Different Styles

So I was wondering how I could paste another navigation menu in but have it a different style as my original. For example, the code of my current one is:

<nav id="site-navigation" class="main-navigation" role="navigation">
			<h3 class="menu-toggle"><?php _e( 'Menu', 'twentytwelve' ); ?></h3>
			<a class="assistive-text" href="#content" title="<?php esc_attr_e( 'Skip to content', 'twentytwelve' ); ?>"><?php _e( 'Skip to content', 'twentytwelve' ); ?></a>
			<?php wp_nav_menu( array( 'theme_location' => 'primary', 'menu_class' => 'nav-menu' ) ); ?>
		</nav><!-- #site-navigation -->

To change the style of it I’ve edited the CSS of the “site-navigation” ID and the “main-navigation” class.

However now I’d like to also place a menu at the bottom of my page but I don’t want it to have the same styles. The problem is, if I change the ID or CLASS of the navigation, the menu for mobile no longer works.