Akitsu Shino has the ability to see spirits from a young age, so when she grows up she joins a secret agency that keeps track of and handles ayakashi. Her job is to make sure to keep the peace between the various ayakashi districts in the special ayakashi town known as Sakuratani.
Ayazuki Mei is a gluttonous high school teenager who runs into some do-M wacko named Charlie at a magic show at her local summer festival. Charlie throws her into his magic box and when she comes out, she finds herself thrown back in time into the Meiji era! They’re both hungry so they sneak into a fancy Rokumeikan building but instead of roast beef, they run into famous Meiji era historical figures! So now Mei gets to choose which historical bishie she gets to snag, while dealing with the fact that she’s completely lost all memories of her present time self. On top of this, she magically gains tamayori powers and can see dead people.
01/30/2020 – I’ve updated it to add Iwasaki Tosuke’s route from the Vita port/mobile game. Original review was from 2014.