The two sisters have a very close relationship. Both Kaguya and Yuzuru care more about the other than themselves. It is noted that while Tohka becomes unstable when separated from Shido and Yoshino becomes unstable when separated from Yoshinon, they only become truly unstable when separated from each other.
Since they were originally one spirit named Yamai, they were originally challenged with the knowledge that only one of them could be allowed to ultimately become the new Yamai, meaning one of them had to die, they both chose to let themselves die rather than the other and they were more than willing to force the other to go along with it. They were overjoyed when Shido found a way they could both survive.
During Volume 8, when Yuzuru disappeared, Kaguya initially panicked and was only calmed down when Ratatoskr told her that she was having a medical examination, which was a lie. However, when Kaguya and Shido went bowling Kaguya revealed that she had seen through the lie and started to cry out of worries for her sister until she was calmed by Shido. After she discovered that Yuzuru, and many other of her friends, had been absorbed into Haniel by Natsumi as part of her "game", Kaguya became enraged to the point she tried to attack Natsumi to get Yuzuru back, but was stopped by Kotori. After Shido won Natsumi's "game" and Yuzuru, along with everyone else, was released from Haniel, Kaguya tearfully embraced her sister.
While Shido treats the Yamai sisters as friends and close acquaintances, the Yamai sisters claim that Shido is their "shared possession". However, it is hinted that their affections toward Shido are much stronger than before.
The Yamai sisters get along very well with Tohka, especially Kaguya, because of their similar energetic personalities. Kaguya refers to Tohka as her kinsman.
While Kaguya's relationship with Origami is unknown, Yuzuru got along well with Origami. This is mainly because of their similar quiet personalities and because Origami gave Yuzuru some advice to help seduce Shido. Because of this, Yuzuru refers to Origami under the nickname Master.
After discovering the two are Spirits (in Volume 7), Origami now views them as enemies. However, even after Origami tried to kill them (in Volume 10), Kaguya and Yuzuru still treat her as a friend. Both of them were shown to be happy now that Origami no longer sees Spirits as enemies, although Kaguya did express she wanted payback for the previous timeline.