Food-delivery companies are adding supermarkets and convenience stores to their order queues.

DoorDash Inc. and Postmates Inc. are among the companies striking deals beyond restaurants to expand their reach and revenue. In doing so, they face competition from rising food sales at Amazon.com Inc., from grocery-delivery specialist Instacart Inc. and from online supermarkets such as FreshDirect LLC and Koninklijke Ahold Delhaize NV’s Peapod.

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