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Champ, Eileen and Max just got home from school. Champ, 11, heads to the living room, removes his shoes and—swoosh—takes the metal slide to the basement.

On this lower level, their parents, Keith Baumgarten and Sara Keane Baumgarten, have built a vast playland for their four children, ages 4 to 11, in their 13,000-square-foot home in Sioux Falls, S.D. Here, the children practice classical guitar, mixed with some piano and percussion, on a stage flanked by velvet curtains. In a hidden room beneath the stairs, decorated…