Sure. Just add the subdirectory and then in your .htaccess file (in the base directory) add, before the index.php redirect lines another redirect something like
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteBase /
RewriteRule ^/otherdirectory/(.*) http://www.yourdomain.com/otherdirectory/$1 [L]
</IfModule>
Just make sure you dont have any url’s using otherdirectory in your wordpress installation.