I have checked out TeamPass and it's a really nice self hosted password manager. It has some solid permissions management. However, the UI is terribly slow and cumbersome. I would use it were it not for the crap UI.
The other options are desktop applications, and while we could distribute a shared password db to all of our employees, that sorta becomes a nightmare to manage and maintain. We did that at the last company I was at. People do all kinds of dumb oops with it. Like store personal passwords which are then overwritten because we push out a new db. The biggest headache is when we need to add a new password, it has to go to some gatekeeper to add it, and then redistribute the db to everyone.
I am thinking of rolling out a very simplistic internal web based password manager that ties into our existing clients manager. I created a prototype of one it definitely seems doable and realistic.