Itachi showed four abilities, the three you named and Kagutsuchi. Itachi extinguished the flames of Amaterasu during his fight with Sasuke.Sasuke has Amaterasu, Kagutsuchi, and Susano'o
Itachi had Amaterasu, Tsukuyomi, and Susano'o
Shisui had Kotoamatsukami in both eyes and presumably Susano'o (It was never shown in the manga, but his Susano'o was designed by Kishimoto himself. It could be seen as a "what could have been" if Shisui survived long enough to actually show it. Whether you want to count this is up to you. Though even if you don't, many Uchiha had both Mangekyo and no Susano'o yet so it doesn't matter). There is no details on his eyes and if each eye had some variation to it, like Obito's
Obito had Kamui in both eyes(Left eye being a self-effect of passing through objects and sucking in himself+anything he touches. Right eye being ranged effect that can suck in something farther away without needing contact.) and presumably Susano'o(Kakashi was able to use Susano'o with both eyes. It's reasonable to assume Obito would have been able to as well if he was in better condition).
Perceiving time slower, casting genjutsu, and copying other abilities are things that any Sharingan can do. It's not a Mangekyo power, rather a Sharingan ability.
Izanagi and Izanami are also not Mangekyo powers, as Danzo was using ordinary Sharingan to cast Izanagi. Itachi just happened to have an activated Mangekyo when he used Izanami.
Sharingan abilities =/= Mangekyo powers.
We know extinguishing the flames is a part of Kagutsuchi and not Amaterasu because Sasuke casts Amaterasu with his left eye, but extinguished them from his right, the eye that holds Kagutsuchi.
I know what Shisui's and Obito's powers were. Not counting Susano'o, they both had one jutsu. Doesn't change a thing I said, it shows that the number of jutsu doesn't have to be three, and Itachi extinguishing the flames, a trait of Kagutsuchi, show it can go as high as four.
Let's call them what they are, not powers, but jutsu. A single Sharingan can have multitple Genjutsu, ninjutsu and kinjutsu in them. We've seen this time and time again, a Sharingan isn't limited to one jutsu per eye, so what you're saying makes no sense. We don't have ANY established limits on how many Mangekyo jutsu a single eye can have. The fact that Itachi exhibited the power to extinguish the flames AKA Kagutsuchi on a far weaker form than Sasuke's, is proof that more than one Mangekyo power can rest in one eye.