There's many ways this whole thing could go but what I would like to see is Asumi and Nao getting gradually more romantically involved until they're p much dating and then Asumi suddenly finds/meets Mai, for some quality triangle shenanigans that lead to a tasty triad in the end.
Asumi wants to get closer to Mai now that she's finally found her but also likes Nao.
Mai equally wants to get closer to Asumi but likes her job and doesn't want to quit.
Nao wants to keep being with Asumi, struggling with jealousy at first but gradually opens up to it, probably with the help of trying out a reservation (with Asumi maybe or without her to see what's up with the whole thing). Maybe she books Mai first before Asumi finds her and develops a bond with her through that
And in the end all three start dating in a cozy polyam triad and enjoy the bounties of lesbian prostitution together forevermore. the end :D