Such a book is necessary.
The trick is that 3I is decentralized. So when you are talkng about 3I you would need to define what impacts 3I as a whole and what is a local (Sector level).
Some items that are of import to the Imperium as a whole in detail. Some of it has been given a few sentences, others whole books have been written.
In no particular order:
The ISS - Get into its mission in detail, High level organization structure. The Reference system (if it is in this version).
X-Boat Network - It's importance to the 3I. Talk about the J4 network, the J6 network (if it is truly around, functional and such). What information gets passed around. Develop time tables for data arrival times (like a message getting from one Sector to another)
The Imperial Navy - It's actual structure and organization, the nature of Depot systems. Imperial Navy High Command (or whatever). What each Sector fleet is designed to fight/defend against. Talk briefly about the interaction of Subsector and Local Navies.
The Imperial government - Describe actual powers of the Emperor, the noble family, how it came to be, who they are. Succession rules as of 1105 (we won't talk about 1116 happening or not
). The Moot and it's powers or not. The actual structure of the bureaucracy. What Arch-Dukes are and what they do.
The Neighbors - Describe the other powers, who if anyone comes around to talk to the Imperial throne (Zhodani ambassador, Solomani agent abroad, Hiver delegation, whatnot) if any.
I recall there have been books in many games that provide a Gazetteer format to describing countries in a one world fantasy setting. For the 3I, it could be done at the Domain level, or Sector level depending on how much would be written.
A Sector could be described as such
Sector xxxx (Part of the Domain of YYYY)
Duke: (Give their name, age, other details)
Sector Capital: (Name the World and UPP)
Explored: (Year ISS first came to the area)
Incorporation: (Year Sector was incorporated into 3I, perhaps date first Duke was given title)
Population and Major Worlds: (UPP's and Locations)
Navy: Location of Depot System, and other Major Naval Bases
ISS: Primary Scout Base location
History of the Sector
Sector's Primary Concerns
Describe a "minor alien race" or two (as was done in Deneb Sector)
Feel and flavor of Sector (i.e. Roleplaying opportunities!)
References to specific Mongoose Books you need if you want to know more