It's possible to add activities to Quotations, Purchase Orders, etc. (in the "chatter).  Users can then see reminders on the top of the screen with a count of activities that are Late / due Today / Future.

In a multi-company database, if a user clicks on that link they will only be able to see the Quotations for the current company (which is what you would expect) and in Odoo 11 and 12 it's only possible to have one current company.

Is there any way to see more information about the reminders for other companies?

I checked mail.activity and it doesn't have the company ID, so I can't think of any simple solution!