United Parcel Service Inc. is adding “peak” surcharges for companies that have been inundating its delivery network with many more packages and oversize items during the coronavirus pandemic, an unprecedented move to manage a summer flood of shipments and higher costs.

UPS typically imposes extra fees on merchants during the busy Christmas shopping season, but—for the first time in the e-commerce era—will add such surcharges starting May 31. The fees would apply to large online sellers like Amazon.com Inc. as well as traditional…

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