The word 'menage' is borrowed from French, where it means 'household'. Their menage includes three generations living under one roof.
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Broader Scope
'Menage' can imply the daily life and interactions within the living arrangement, not just the people. The sitcom focused on the hilarious daily menage of a quirky family.
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Not Just Families
'Menage' is not exclusive to traditional families; it can refer to any group sharing a living space. Their student menage was always busy with activities.