"The genitive forms whosever and (informal) whoever's are possible but rare in the free choice construction. Thus Take whosever/whoever's you like could serve as a response to the question Whose bicycle shall I take? The genitives are not admissible outside the free choice construction -- cf. *They want to question whosever/whoever's dog was barking throughout the night or *Whosever/Whoever's car is blocking my driveway must move it immediately. The close grammatical association between the genitive determiner and the following head noun seems to suggest the anomalous meanings where it is the dog they want to question and the car that must move itself."
-- CGEL, p. 1075