If there’s a retail sector that has barely gone digital, you can bet Amazon is trying to crack it. In the case of beer and alcohol, a startup called Drizly is moving fast to try to beat Amazon there.

Since its founding in 2012, Drizly has let shoppers order beer, wine and alcohol through the Drizly mobile app and get it delivered from local liquor stores in under an hour. Now, the Boston-based startup is adding next-day, scheduled delivery as an option, which it says will let it drastically increase the number of liquor, wine and beer brands it can offer through its app.

The goal is to build the biggest online catalog of booze available for delivery in the country, so that someday it becomes the de facto e-commerce shop for online alcohol sales. Eventually, Drizly plans to add price-comparison tools, too — not a novel concept in many e-commerce categories, but something that is not yet common in the alcohol industry.

“It was never just about on-demand,” CEO Nick Rellas said in an interview. “It was actually about e-commerce and doing in alcohol what has happened in books and CDs. But we had to be humble about that because we’re a little tech startup.”

Drizly, which has raised more than $17 million in financing, has 58 employees and operates in around 20 markets. The startup makes money by licensing software to liquor stores that allows them to accept orders from the app. These annual licensing fees typically work out to between 5 percent and 8 percent of Drizly-sourced sales, though they are not tied directly to a specific cut of transactions.

Drizly believes an exclusive relationship it holds with the Wine & Spirits Wholesalers of America trade group, which has invested in the startup, gives it a distinct advantage in what is a highly regulated industry. Some of the group’s alcohol wholesalers are now allowing Drizly to display all the alcohol they carry in their warehouses, versus just what is available in local stores. That should eventually give Drizly access to tens of thousands of different alcoholic items, Rellas said.

If a local liquor store doesn’t carry it, a Drizly customer can now order it anyway and have it delivered the following day. This new service is only currently available in Boston and Washington, D.C, but should expand to five new markets in the next three months.

Today, shoppers in the U.S. don’t have many options to order a wide selection of alcohol — outside of wine — from a single site and get it delivered to them the following day. Services like Instacart, Delivery.com and Minibar partner with local stores, in part because of alcohol industry regulations, and typically specialize in same-day delivery.

Amazon currently delivers alcohol in three markets — Seattle, New York City and San Diego — through its one-hour delivery service, Prime Now. In Seattle, it has its own liquor license, while in the other two cities it partners with local liquor stores. In an ideal world for Amazon, you’d think it would want to circumvent local stores as well as wholesalers and buy booze directly from the companies making it. But laws created in the wake of Prohibition make that difficult, which is why Drizly’s relationship with wholesalers appears to give it an advantage. For now.

Still, the expansion by Drizly also underscores the challenges some on-demand companies can face building a big, sustainable business solely around immediate delivery. Other on-demand startups like Shyp, which picks up and mails packages for people, have also moved some of their business away from instant delivery and to scheduled pickups.

In the case of Drizly, Rellas said there are only so many people who want booze right now, and only so much inventory that local stores carry.

“There are a ton of constraints with on-demand,” he said. “Stores have to deliver fast, and consumers have to want it now.”