Grant editor settings to a member


I have a multisite and I would like to give to certain users the option to open a post with their business details (kind of index) and I would like to grant to each user the option to edit its own information on 1 post (the one with their information) but not to any other post, page, etc.

All the content (including these posts) will be available to see by all public. Is this possible to do with this plugin? Or do I need a different plugin?