No the Dom way to get it is during the outdoor pool scene with Olivia and Alessandra. When you massage Alessandra you have to pick her feet, then she basically asks you if you like to be submissive in the bedroom. When you say yes ==> SecretSub.
The other way is to start as K3/K4 and getting promoted into dom route. Then there is a indoor pool scene with Alessandra (that girl really likes pools) in which she basically wants you to submit to her. If you do it ==> SecretSub.
She will always make you K7 regardless of your current rank later. And yes that means if you are K5 you will be K7 but also if you are K9 you will be K7. I guess it was done for the housing, so Tess didnt need to create the same scene with different locations. But feels kinda weird, because Alessandra tells you she wants you to become strong outside of your relationship, but deranks you ...

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I like SecretSub a lot but not so much because of Alessandra but rather Angelica
. SecretSub can be both kinda harsh and pretty gentle depending if you romance Alessandra or want to become her pet. My only real critique of SecretSub path outside of the deranking is that Alessandra still is super degrading towards Kane. I mean I get that Tess most likely has a massiv degrading fetish, but I think it would have hit harder if Alessandra would be more supportive and less demanding. Like Kane will rule the world, but will always be kneeling for her. I feel it would show much more confidence of her if she accepts him as the only male (except Alexander) who is equal to her, but just can't resist to server her in the end. I mean dominating a pathetic worm is much less impressive than dominating the literally King of the world
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To your question: No, you always only get two rooms, except if you get the court room scene.
To your spoiler:
I still feel more like it's Alessandra since she only seem to have significance on SecretSub. But yeah Juliette would be also my second guess.