You can manage this via the template_include
hook.
add_filter( 'template_include', 'cats_and_dogs_living_together', 99 );
function cats_and_dogs_living_together( $template ) {
if ( is_post_type_archive( array ( 'cat', 'dog' ) ) ) {
$new_template = locate_template( array( 'archive-dog.php' ) );
if ( '' != $new_template ) {
return $new_template;
}
}
return $template;
}
Hope this helps!