As your mention of It Happened One night, with Ellie dressing in his
nightclothes and Gable adopting the apron and mien
of a fussing mother, most screwball comedies employ crossdressing, etc.
as a generic characteristic. It typically
functions to allow a character to grow by adopting a perspective
outside the culturally predetermined  one of gender
and to discover other aspects of identity. It thus prepares for the
reconciliation of the two screwball lovers whose
initial antagonisms had both attracted and kept them apart. Good
examples of this would come to me later in the morning.
 
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