Numbers work because single posts can have pagination, and there is a rewrite rule to support that.
If you want to add an additional parameter after a permalink, add a rewrite endpoint.
add_rewrite_endpoint( 'show', EP_PERMALINK );
EDIT- Here’s an internal rewrite example, assuming your custom post type slug is type1
:
add_rewrite_rule(
'c/([^/]+)/([^/]+)/([^/]+)/?$',
'index.php?type1=$matches[1]&type2=$matches[3]',
'top'
);