Select Peloton stores in Texas, Florida, Minnesota and Denver will for a limited period offer a bike and subscription for between $60 and $100 a month, an experiment that aims to find a price proposition that will help return Peloton to profitability without crippling growth.

If adopted, the model would be a major shift for Peloton, which built a business around selling high-price, screen-equipped stationary bikes alongside $39-per-month subscriptions to its connected workout classes. The idea: sell Peloton as a fitness service that can be canceled anytime rather than as a major purchase with a subscription attached.

“There is no value in sitting around negotiating what the outcome will be,”

Barry McCarthy,

who last month replaced co-founder

John Foley

as CEO, said in an interview. “Let’s get in the market and let the customer tell us what works.”

Along with a pricing overhaul, Mr. McCarthy, the 68-year-old former finance chief of

Netflix Inc.

and

Spotify Technology SA,

said he plans to reshape his executive team, consider manufacturing simpler bikes, and upend the company’s capital spending strategy. Rather than investing primarily in bikes, treadmills and other equipment, he said, Peloton will spend most of its money improving its digital interface and content options.

He said inventors that control 70% of voting shares of Peloton, including Mr. Foley, have agreed to put off any discussions around selling the company while he executes his turnaround plan. Mr. Foley still controls around 35% of voting power even after selling about $150 million worth of his shares in the company since the start of 2021, said Ben Silverman, director of research at InsiderScore. That voting power is because of his holdings of Class B shares, which entitle holders to 20 votes a share.

Initially one the pandemic’s biggest success stories, New York-based Peloton has lowered its revenue forecasts for several quarters in a row and has said it would cut roughly 20% of its corporate positions to help cope with widening losses as demand cools.

The $39-a-month subscription price has existed essentially since Peloton’s inception. In recent years, the company has lowered the cost of its bikes and treadmills, either by cutting prices or offering cheaper options. A Peloton bike in 2020 cost $2,495; now the cheapest model is $1,495, not including a delivery charge.

Under the test program, people get a Peloton and a membership that includes access to all its courses for a single monthly fee, with the ability to cancel anytime. The offers would be available through Peloton stores, or studios, and not online. Subscribers would pay a nonrefundable delivery fee.

Mr. McCarthy said a different pricing system could draw new customers and make the business more profitable.

His predecessor, Mr. Foley, argued that Covid was only the beginning of Americans’ shift to online, connected fitness. Based on that assumption, Mr. Foley dramatically increased the company’s capacity, which proved to be well in excess of demand as legions of people returned to gyms and Peloton’s growth sputtered

That misstep, Mr. McCarthy said, led to Peloton’s current woes.

Now, he said, Peloton has to figure out how to tap new customers and make more money on each subscription, while reducing its reliance on bikes and treadmills to deliver profits.

Given Peloton’s ability to retain subscribers, Mr. McCarthy said, higher subscription rates carry big profit potential over time. Even at $39, Peloton subscriptions are hugely profitable, he said. He said he wants to employ models that succeeded at Spotify and Netflix and that Peloton has far higher retention rates than either of those companies.

“I’m a huge proponent of them charging more for subscriptions,” said BMO Capital Markets analyst Simeon Siegel. “But they need to internalize that that will hurt their brand and lower demand,” while making the company more profitable.

He said the fact that Peloton’s growth has slowed dramatically despite cutting the price of equipment casts doubt on whether any changes to the pricing model will win converts.

A Peloton spokeswoman said the ability of customers to cancel anytime differentiates the potential new model from previous price cuts.

Profitability of Peloton’s exercise equipment is sharply lower than it was before the pandemic, as the company struggles with higher production and logistics costs and excess capacity.

Equipment sales have been vital because the physical machines, while more costly to make, generate more than twice as much revenue as subscriptions, UBS analyst Arpiné Kocharyan said.

Equipment sales have funded Peloton’s ballooning marketing spending up until now, Ms. Kocharyan said. “If you are going to get out of the product business, who is going to pay for that sales and marketing?” she said.

Mr. McCarthy said it isn’t yet clear the role Peloton machines will play in the company’s future. He said roughly 80% of capital spending goes toward equipment, with the rest spent on software. That should be reversed, he said.

Among potential offerings he thinks Peloton should look at developing: its own social-media platform, more seamless ways for members to interact and compete with each other during classes, and partnerships that could land Peloton classes on other devices, or allow outside content to stream on Peloton’s screens.

At the moment, Mr. McCarthy said, Peloton will fervently market test, a strategy more reliable than focus groups and consumer surveys. Netflix also did market tests to see what caused subscribers to ditch the service or keep it, he said.

There isn’t much middle ground between success and failure, he said.

“Either I’m going to leave here successfully,” he said, “or I’m going to leave with a greatly diminished reputation.”

Write to Sharon Terlep at sharon.terlep@wsj.com