For the 2nd anniversary of Kantai Collection (April 2015), Mutsuki, along with Kisaragi, gained a second remodel/kai ni form.
They now feature a dark blue jacket with their names (+ Kai Ni) on the sleeves and a crescent pin on both the jacket (both at the same place) and the serafuku, now with a red scarf. On their rigging is a flower, like Uzuki and Yayoi, bridging the later design with the earlier one. They also come with a 12.7cm twin gun mount along with their standard 12cm single gun. This remodel is noted to be completely fictional, however, Mutsuki having been sunk relatively early in the war (during the Guadalcanal Campaign). Mutsuki herself has the crescent pin on her serafuku scarf. Her flower is a camellia, flower of her namesake month (January).
This tag implicates mutsuki_(kancolle) (learn more).