NEW YORK — With e-commerce capturing a growing slice of the retail pie, the future of the physical store becomes a more urgent question.

Coresight Research tackled the issue in the third and final installment of its “Retail Reworked” series, focusing on areas of opportunity for brick-and-mortar retailers in a time when more and more purchases are made digitally.

The report concludes that physical stores can benefit by focusing on one or more of the following propositions:

• Convenience — serving demand for last-minute purchases in local stores.

• Collection — offering in-store pickup of online orders, which can lead to incremental purchases by shoppers who visit stores to collect their orders.

• Discount — serving the shopper base that continues to flock to value-positioned stores operating largely or solely offline, such as off-price stores, grocery discount stores, warehouse clubs and dollar stores.

• Destination — creating experience-rich, quality stores and shopping centers that appeal to leisure shoppers.

“We expect e-commerce to continue to grow its share of retail sales in the coming years as it peels away substantial volumes from store-based retailers, mainly in nonfood categories,” state the authors of the report.

Coresight Research expects that e-commerce could realistically capture 40% or more of all clothing and footwear sales in the United States in the 2030s.

The authors assert that e-commerce is likely to capture the largest share among those purchases that are planned, functional or higher-value.

This leaves physical stores to fill in the gaps for consumers whose shopping mission would not be best served by ­e-commerce.

“Stores that cater to time-pressed shoppers looking for immediate purchases will be among the most resilient physical formats,” the report said.

“Online delivery options will get faster, and more e-commerce operators will offer same-day, two-hour and one-hour delivery, but shoppers will still encounter barriers to buying online when they need products fast. Consumers outside dense urban areas are already much less likely to be served by rapid delivery services, and such services still tend to carry significant charges, which makes them unavailable for lower-value purchases and for frugal shoppers.”

Demand for convenience will be most evident in grocery retailing, the report said, as shoppers will always want to be able to replenish the basics and choose dinner for tonight on short notice.

But shoppers also often find themselves needing unexpected gifts and replacement items, and these needs, along with treats that are bought on impulse, will drive demand for last-minute, store-based purchases across much of nonfood retail.

The report notes strong demand for in-store collection of digital orders.

“[Grocery] retailers are currently racing to roll out pickup points as collection, rather than delivery, is becoming the default option in the nascent U.S. online grocery market,” according to the report.

Dollar stores, warehouse clubs and off-price retailers operate largely or solely off-line, and even if more of these businesses introduce e-commerce operations, Coresight Research expects that their sales will remain disproportionately store-based due to customer demographics, customer resistance to delivery charges and the challenges of replicating their retail experiences on the ­internet.