Koishi is occasionally drawn with some sort of connection to Flandre Scarlet, since both are extra-bosses who are the younger sisters of the owner of a mansion from the same game.
Since many aspects of Koishi are references to psychology, there's a running joke that her "Embers of Love" spellcard is a reference to the phallic obsession of Freudian psychology. For those that do not get the hint, look closely at the shape of the bullets. Of course if you think that, maybe Freud was right.
Satori's design can also be referenced to all the bosses in Ibara, as both Koishi and the Rose sisters have white hair and has a lot of reference to roses (although roses in Ibara are point items instead of bullets)
A lot of fanart of Koishi references Glico, the Japanese snack company behind Pocky, due to the pose she strikes while firing. Glico's logo is a finishing track athlete with arms raised in mid-stride. It was created for their very first product, a line of caramel with the slogan "300 meters in every piece." Each piece has the estimated energy for a 300 meter run (15.4kcal) and is today sold in heart shapes.
Another common running joke is fans drawing Koishi in the style of the "Koishi Komeiji's Heart-Throbbing Adventure" series by Sentaku-bune, or fans referencing quotes from it such as "My hat is my friend, it helps me relax".
Similar to Kahlo's painting mentioned above (The Two Fridas), some fan works display the cord(s) to her third eye being of having already been cut, while Satori's remains intact.