TML Multisite question about redirecting to different site after login

Hi,
First off, thanks for the great plugin. I have used it often on many sites.
Now, I am not even sure this is possible, but when a user logs into our main employee website, we want to send them to a different site (sites are basically department specific content) based on their role. I can’t seem to get the redirect to work when it redirects to a different site. Is this at all possible? I know it would work if they just logged into the specific site itself but I want them to just have one url for the main employee site. I can do this with a redirect on a page within that site but that seems clunky. Sorry if this is confusing,
Thanks for your help,
Danielle

https://wordpress.org/plugins/theme-my-login/