Intertype relations in Casshern Sins - can you identify them?

For anyone who has not watched a short TV show called "Casshern Sins", I highly, highly recommend watching it if you enjoy seeing many different yet deep intertype relationships in one show. I wouldn't want to spoil such a great show for anyone so continue if you don't mind spoilers.

It's important to mention that Casshern (the guy in white) is extremely depressed and suicidal because he killed Luna (the Jesus figure of the show) who was granting all robots eternal life, thus leading all robots to "ruin" (death). By killing Luna, Casshern was cursed with extreme regenerative abilities and immortality. At the start of the show, he awakes with amnesia, slowly finding out what he's done to the world while trying to find a way to atone for his actions, hence the title "Casshern Sins".

Casshern and Dio

Dio and Leda

Casshern and Sophita

https://www.youtube.com/watch?v=ylutP4zuIfw

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Casshern and Lyuze

The most complicated relationship that I think can only be grasped by watching the series (only 24 eps).

Any insights are welcome.

 

I'm typing based off of my knowledge of Jung's Psychological Types, MBTI and my newly (limited) acquired knowledge of socionics so keep that in mind.

Dio is some kind of aggressor, probably ILI or LIE as I think he is a Gamma and an enneagram type 8. He is the character in all of fiction that I relate to the most and see myself in. His relationship with Leda is what comes to mind when I think of Gamma duals. She has her own goals and she's using him to realize them. All Dio really wants is to prove his might, will and strength (Se Super-Id?) against Casshern who has always been one step ahead of him despite being his identical twin, but Leda slowly works him into wanting the same goals as her i.e. world domination and power. If you've watched the show then you'll know just how deep Leda's character goes.

I'm convinced that Sophita is an SEE, possibly SLE but most likely SEE. She comes across as sort of infantile at times (Ne-role?) but she's consistently an aggressor for the most part, even going as far as to outright state her interest in Casshern as soon as she met him.

Casshern and Lyuze are the two hardest for me to type and I go back and forth between a few types for each of them. I have a hunch on Casshern's type but would like to hear other thoughts.

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Intertype relations in Casshern Sins - can you identify them?