The Sky Canopy Dominion or Heavenly Canopy Domain, (天蓋領域 Tengai Ryōiki), formerly known as the Macrospatial Quantum Cosmic Existence (広域帯宇宙存在 Kōiki-Tai Uchū-Sonzai), is the name for a data entity "similar but separate" to the Data Overmind. It exists in another "place". It appears to be just as alien to the Data Overmind as humans are and is unable to communicate directly with the Data Overmind. There hadn't been any contact, because they felt that contact would not lead to any mutual understanding. Emiri Kimidori also mentions that their logical foundation differs from that of the Data Overmind and their Humanoid Interfaces.
It has an unspecified interest in Sasaki and Haruhi Suzumiya.
Kuyou Suou, a Sky Canopy Dominion interface
When Kuyou Suou interacted with Yuki Nagato and Emiri Kimidori, she seemed to create quiet "burning" sounds, causing Yuki to apparently react angrily. She even grabbed Emiri, but eventually let go after Emiri asked her to. (In response, the TFEIs seemed to create quiet sounds as well.) This kind of communication can render Data Overmind interfaces "ill".
Kuyou never needed to "ask permission" from the Sky Canopy Dominion to use abilities. The Data Overmind interfaces theorized that she might be a direct extension of her Dominion.
History
By The Disappearance of Haruhi Suzumiya the Dominion had created an interface known as Kuyou Suou. Her linguistic capabilities were cruder than those of TFEIs such as Yuki Nagato, but was still able to date Taniguchi. When Nagato altered the world, the interface was unaffected.
The first interaction with the SOS Brigade occurred in Snow Mountain Syndrome, where the Dominion, in an attempt to learn about Yuki, placed her and the rest of the SOS Brigade into a scenario where Yuki could not use her powers to escape. In response, the Data Overmind caused her to fall "ill" so she would not understand what the Data Overmind was trying to convey. This prevented the Dominion from learning from her.
Nagato and the rest of the SOS Brigade met with Sasaki and several of her "allies". When they did so, Nagato and Kuyou Suou attempted to exchange information, but were largely unsuccessful. (Kyon believed that Nagato was angry during this exchange.) This exchange would eventually render Nagato "ill".
α Activities
Yuki Nagato noted that it had taken quite a long time (based on the limited communication in that incident) for the Data Overmind to even learn the Dominion's name. (The entity had named it the "Macrospatial Quantum Cosmic Existence".) Nagato believed they could create a humanoid interface and then learn about Suzumiya or even communicate with other interfaces thorough speech.
β Activities
Meanwhile, Kuyou Suou's attempts to communicate with Yuki rendered her "ill" again. Kyon, believing she was behind the illness, attempted to confront Kuyou. Ryoko Asakura was dispatched to prevent Kuyou from approaching Kyon, and the two engaged in combat. Emiri Kimidori then appeared in order to control Asakura. Asakura and Kimidori learned something of her (and Kuyou learned something of them) during the battle.
Combined Timeline
Following the closed space confrontation, Nagato was removed from her post facilitating communication between the Data Overmind and Sky Canopy Domain as the level of communication that could be sustained was insufficient. Nagato's new task was to observe Haruhi Suzumiya and Kuyou Suou.
The two entities moved to "phase two", a mutual understanding phase, using another interface. (Kyon believes this is Emiri Kimidori.)
Meanwhile, Kuyou Suou adopted the goal of achieving autonomy for herself.