If Mitsuki and Hime end up having a serious romantic relationship, Sumika will end up opposing them
While she's largely concerned about what Kanoko might do out of her Unrequited Love
for Hime, she's also concerned about relationships falling apart. A flashback in Volume 3 seemed to imply that two of Sumika's coworkers got into a relationship, as shown by them engaging in a public display of affection in front of Sumika. Apparently, the two girls eventually broke up, causing them to leave the salon- you can see both kreusz necklaces on the table, as Sumika narrates, "that friendly relationship is easily broken." If Sumika worries that Hime and Mitsuki will have another falling out, she may intervene in an attempt to prevent them from becoming a couple, and may have to be talked out of it.
When Mai reveals that she'd lied, and that her arm actually healed at the end of April, Hime will claim that she always knew, or at least knew for a while
Since the story will probably have Hime find out at some point, and is unlikely to play this Internal Reveal for drama, it's likely that she'll claim that she knew all along, possibly because she'd come to love working at Liebe.
Mitsuki had to transfer out of her elementary school due to her family suffering financial hardship
Consider that the Yano family had a Big Fancy House and a maid when Mitsuki was in elementary school, but they're living in an apartment by the time Hime visits Mitsuki in Volume 6. It's possible that they had to sell the house and move away for some reason, thus forcing Mitsuki to transfer schools.