Without modification this is what you are limited to with regards to roles and capabilities:
https://codex.wordpress.org/Roles_and_Capabilities
However there are a number of permissions and membership level plugins out there which may offer variations.
https://wordpress.org/extend/plugins/search.php?q=Permissions&sort=
https://buddypress.org/extend/plugins/?search=User
I think perhaps though your sticking point may be admin check without admin rights though.
Yeah, I’ve tried to look in a few plugins codes to find the current_user_can part and change it to something like add users that my almost-admin role can do, but so far it hasn’t worked.
Actually, I found something that worked. I was trying to let users with some additional abilities use the edit users plugin, I just had to give them the delete users capability…wasn’t an actual admin check. I just didn’t go through all the options originally, and I still don’t really know what a third of them really do. Thanks for your help!
No problem glad you found something.