You should add the Microdata on every page … because of reasons.
If you have a page where your business data is duplicated (e.g., a contact page where the business contact information is in the site header and in the page body), you should only markup one of these instances. Otherwise you’d create two LocalBusiness
entities for the same entity.
If you have a page where your and partner business data is contained, you should mark up each business separately. So each business entity is represented by an own LocalBusiness
entity.