NEW YORK >> American Express will roll out a new loyalty program, Plenti, on Monday, allowing U.S. shoppers for the first time to earn rewards points through a variety of purchases, from paying a phone bill to filling up at the pump.

Unlike other loyalty programs, such as frequent flyer plans, Plenti isn’t tied to a single company or credit card issuer. Users can join for free and don’t have to be American Express members.

Customers will be able to accumulate points through purchases at Enterprise Rent-A-Car, Rite Aid, Macy’s and a number of other companies, which can then be used for discounts at any participating vendor. Plenti points built up by buying gas or a Nationwide insurance policy, for example, could earn discounts on an electric bill from Direct Energy or milk from Rite Aid.

“It will really be the first time where U.S. consumers, on a single program, can take the rewards they’ve earned in one industry and take it to another,” said Abeer Bhatia, chief executive of US Loyalty at American Express.

Loyalty programs aim to keep customers coming back by allowing them to earn points toward discounts or other rewards. But these programs are often tied to one or two retailers and limited in how they can be used.

Plenti’s program is straightforward. A customer signs up at a participating merchant, on the Plenti app for smartphones, or on Plenti.com. Every time a customer spends money, either cash or by using a debit or credit card, they will earn “Plenti Points” after giving their Plenti account number. The number of points a customer earns on a transaction will vary from merchant to merchant.

Plenti Points can be redeemed in 1,000-point increments for $10 in savings, so 1,000 points earned at Exxon could be used for $10 in savings at Macy’s or RiteAid.

Plenti is part of American Express’ push to broaden its reach of customers, which have traditionally been the affluent, the well-traveled and people who have a lot of business expenses. American Express lost its exclusive deal with Costco in January, which was considered a major blow to the company. JetBlue is also reportedly planning on ending its relationship with AmEx later this year.

AmEx already operates loyalty programs in Italy, Germany, Poland, India and Mexico that, like Plenti, have partner merchants across a wide variety of industries. The programs, like Germany’s PayBack, have proved hugely popular. In some cases half of the country’s eligible population participates in the programs.

Some other features of the program:

— WHO’S IN IT: Companies participating in the Plenti launch include AT&T, Exxon Mobil, Macy’s, Nationwide, Rite Aid, utility company Direct Energy and video streaming service Hulu.com. Enterprise Rent-A-Car, which includes the rental car brands Enterprise, Alamo and National, is also joining. American Express expects the network to expand.

—A CREDIT CARD: AmEx is launching a co-branded credit card, known as the Plenti Credit Card by American Express, that will allow customers to earn one Plenti point for every dollar they spend, regardless of whether the merchant is part of the Plenti network or not. American Express cardholders who are part of the Membership Rewards program will be able to convert Membership Reward points into Plenti points.

— GROCERY STORES: Customers will be able to link their grocery store loyalty program to Plenti, and earn points for Plenti through everyday spending at stores.

— PRIVACY: Plenti will not share transaction data between retailers. Rite Aid will not know you what you bought at Macy’s and vice versa. Plenti members will be allowed to opt-out of marketing offers.