Yooooo you’re actually cooking with that angle theory! The sisters are one thing but the press and media catch wind of this? My brother in Christ .. it’s really going to get CRITICAL in the Shiunji household.
Realistically, any society where money = "worth in every aspect" means that fiscal might makes right.
And, if the six of them (Arata + Five Sisters)
only want to live as a family harem unit and aren't creating sex dungeons or throwing orgy parties where they rope other random people into their nonsense, then there's not a whole lot that could legally be done to them. They could even go without state-recognized marriage, or have Arata marry one, and do the equivalent of Common Law unions for the rest. So that legally there's one person who could make medical decisions and the like, but otherwise they just live their lives how they want.
And the sheer amount of wealth behind them, especially if Arata takes over their adoptive father's business in some significant capacity, means that they sit in a caste of society that gets a lot of leeway for "doing what they like".
There'd be issues if they were doing criminal or
deeply immoral stuff that involved other people outside their group, but I reckon that everyone around them would just go "yep that's the weird Shiunji Family, they're all together but it's just harmless rich people weirdness". And that's assuming the author wanted to do this
and ground it in some sort of realism.
Even the media would treat as sensational, but they'd get bored eventually if nothing scandalous keeps happening (sex parties, roping in others, etc). Rich people being weird with themselves in their own homes loses public interest pretty quickly, after all.
I don't think it will go that way, or has to, or even would be a good idea to do so. Arata getting with one of them and the rest simply remaining family, or even all going their own ways, would be just as valid an ending, in my mind.
But the option's there and it's been soft-justified from the start.