WASHINGTON—The Trump administration is scrambling to develop a plan for how Americans could return to work in a few weeks without exacerbating the spread of the new coronavirus in the U.S., even though the president’s authority over reopening the nation faces sharp limits.

White House advisers and public health experts are developing proposals that could include workplace testing of employees and intensified contact tracing to curb the spread of the infection, according to people familiar with the planning. Their goal is to…

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