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Chris Burch, the venture capitalist who co-founded the fashion brand Tory Burch, has bought a Miami Beach home in an off-market deal for $12.5 million.

Mr. Burch, who has been a Miami Beach resident for some time, said he plans to tear down the existing house and build a new home on the site to serve as his primary residence. The roughly 1½-acre property has about 170 feet of frontage on the Indian Creek Canal with a dock, and…