If we bring other organizations into our current database, can they have different DTDs than we do?
Tridion Docs is based and configured out of the box on the OASIS DITA XML model, which includes the various DTDs for maps and topics within your system. Specific DITA DTDs are referenced within the templates when a user creates a new object, such as a Concept or Task topic, DITA Map, etc.
To promote content reuse and other system benefits, all teams must use the DITA standard for their content. However, it is possible to create various templates that reference the same Task DTD. For example, a software group in your company could have a template for a "Task for software" and the hardware group a "Task for hardware." Each template would have different placeholder text and other items unique to their needs. They do share the same Task DTD (FYI, there are a few different DITA Task topic types).
Optionally, Tridion Docs can be configured to support DITA Specializations if you need specific changes or new topic/map types.
Tridion Docs cannot be configured for other XML standards, such as DocBook.