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Almost every week, Jeremy Schaller gets a call from a developer who wants to buy the two unremarkable four-story buildings that house Schaller and Weber, a German sausage and sauerkraut landmark on the Upper East Side of Manhattan.

One developer even offered him $24 million, almost quadruple the market value of both buildings.

The developers, Mr. Schaller and preservationists believe, want to demolish the buildings and add another soaring tower to the Yorkville neighborhood landscape that historically was composed of working-class walk-ups and mom-and-pop shops, though dappled with expensive terraced high-rises of more modest scale.

But Mr. Schaller has turned every offer down, even those that promised he could reopen the store in the proposed tower.

“This store is iconic and its aesthetic would be compromised if we knocked down the buildings,” said Mr. Schaller, 40, the third generation of Schallers to run the shop.