Make a private wordpress plugin centrally updated

Hi everyone,

We are currently discussing the best way to make a plugin which we are going to use across many of our multisite networks. The plugin will need to be private, it would be of no use to anyone outside our organization in any case.

We want to make it as easy as possible to maintain. So we want to be able to update one copy of the plugin then the admins of each multisite could just hit the standard update from their wp-admin.

Is there a way to make a private WordPress plugin that isn’t listed in the plugin directory but can be updated using the WordPress network?