Mark Tritton arrived at Bed Bath & Beyond in 2019 with a plan to revive the home-goods retailer and ward off competition from Amazon.com Inc., Target Corp. and other large chains: sell what nobody else has.

Switching to private-label brands has worked for many retailers. At Bed Bath & Beyond—beloved for its 20% off coupon and massive product selection—the changes alienated customers and sent sales into free fall.