The inter-dimensional building
The headquarters are immense and got a foot in every explored dimension. Even today the agency claims the first construction built after the exploration as its own and links it to the main complex. On twenty of them though, it is way more than a mere outpost. The unending office of Myrella III, the explorers' training grounds of Decemer IV, the cutting-edge facilities of Tianmen Prime and Op IV; every major complex after the Terran one is specialized to get the maximum efficiency out of it. The latter is now the core of the organization, centralizing the directions of sections and head administration, as well as countless smaller departments that never moved out due to administrative oversight or shenanigans.
Overall, the building is supposed to be the size of a small world, and is ever-growing. At least a couple of hundred people are required to manage a dimension properly, and way more if the dimension gets colonized. There needs to be enough room for the offices, the pause rooms and all the amenities required by Terran law. Every new dimension is a puzzle of reordering things and people when new aisles are not added altogether. The world of Myrella III, exclusive to the agency, is slowly getting swallowed by the building.
When a building is too big for the human mind to apprehend, it is obvious that people will get lost. Local plans are all over the place, and multiple navigation applications were developed. When even those fail, the lost person can turn to one of the hundred guides, hired to help the employees lost in the maze of hallways and elevators. Since it would be impossible to travel between two departments by foot, manned shuttles, automated trains and hyperspeed elevators are always a flight of stairs away. Big hallways work like streets, special rooms are hubs and stations, and even shops have made their way into the building, providing food and other goods.
Ok, I see your route. Are you in a hurry? Under an hour? That won't do ma'am, best I can do is one and a half, but you'll need to run. Don't worry, they'll understand. The record for the track from Decemer IV to the archives is fifty minutes, mad lad was sprinting with biofluid boots all along. Got suspended after that, of course. Injured three co-workers on the way. Oh yeah sorry, I got distracted, so from where you are, you should see a door with a red "AX-18" glowing neon above. Go through, then turn right first chance you get, walk straight for five hundred meters and you should see a blue line painted on the floor. Get a shuttle to follow it for two kilometres, then...
The only thing that the headquarters seem to lack is lodgings. It may be strange for such a huge complex to contain an amusement park and not any apartment, but this is on purpose, to avoid the many constraints of the status of Hypercity on Terra. They got all the characteristics except for this one, which is not planned to be added anytime soon. Sleeping at the office is totally allowed though, the break rooms have all the comfort needed.
Having a building in several dimensions at the same time is not common. In fact, only the I.D.E.A. pulled this feat off and set an intricate precedent for how the law should apply. Local governors tried to bind the headquarters to their rule, but at the end of the day, the interdimensional court ruled that since the original building and the head of administration resided in Terra, the law of the capital was the only one that should apply inside the building. This decision was directed and welcomed by both the I.D.E.A.'s board and employees, the former for the great reduction in paperwork and the second because Terran laws were one of the most protective toward workers.
Naming rooms and aisles
On Terra, even the biggest companies fare well with the good old "letter-number" naming scheme for their buildings, usually not going over two digits. From A1 to Z99, there is more than enough for all complexes except the unreasonable I.D.E.A. When the classic naming scheme showed its limits, another one had to be found, but the decision was far from unanimous at the time. As a result, over thirty schemes coexisted for a time. Most of them disappeared in a few months, but the rooms and hallways never got renamed. To add up to the confusion, four standards still coexist and new ones appear from time to time.