WASHINGTON—As President Donald Trump considers new tariffs on imported vehicles and pursues a deal with China to avoid a trade war, economists and business leaders see a pattern emerging in the White House’s efforts to renegotiate many trade relationships: Open aggressively, then settle for incremental concessions.

The Trump administration has accused U.S. trading partners of taking advantage of an open U.S. economy. Mr. Trump has demanded partners—China, Mexico, Canada, the EU and others—rewrite trade relationships in ways...