This wouldn't be an orgy. It's normal group sex. Nothing about it is preplanned nor is three people enough for an orgy.
There is that sister who might also get involved.
Sonoe wants Ichika, but settles for Shiori.
Shiori wants Rei, but settles for Sonoe.
Rei is after Ichka to mess with the other two.
Ichika wants Sonoe, but she's avoiding the drama - for now.
I think the only way this gets solved is if everyone fucks everyone.
(including the incest - those hostile sisters could use a bonding activity to get over their differences...)
Round 1: Shiori X Sonoe + Ichika X Rei
(the bonding of seconds)
Round 2: Shiori X Ichika + Sonoe X Rei
(the bonding of sisters and friends)
Round 3: Sonoe X Ichika + Shiori X Rei
(the bonding of lovers)
Round 4+:
The circle of degeneracy...
...and then they all lived happily ever after.