Many businesses have treated $Amazon.Com Inc(AMZN.US)$ and $Microsoft Corp(MSFT.US)$ as the only options as they look to embrace cloud-computing. But IT managers now are realizing they have leverage in an increasingly competitive industry.

Businesses and governments are signing up for a mix of providers, cherry-picking features and playing the vendors off against each other to keep costs down, company executives and cloud analysts say. It is opening up business opportunities for runners-up like $Alphabet Inc-CL A(GOOGL.US)$'s Google, $Oracle Corp(ORCL.US)$ and $International Business Machines Corp(IBM.US)$, though Amazon and Microsoft remain dominant and still account for the lion's share of cloud revenue.

Credit-reporting firm Experian PLC began its move to the cloud with Amazon Web Services in 2014. It has since added services from Microsoft, Google and more recently Oracle, whose technology it had historically used in its own data centers, said Mervyn Lally, the global chief enterprise architect at Experian.

"More options are good," Mr. Lally said, adding they create competitive pressures "we want to take advantage of."

Companies such as AT&T Inc. also are stitching together a network of vendors, including Microsoft, Google and others.

"We're seeing more and more customers adopt a multi-cloud strategy simply because some workloads run better or more cost-effectively on different clouds," said Clay Magouyrk, executive vice president of Oracle Cloud Infrastructure.

World-wide spending on cloud-computing infrastructure services rose about 32% last year to $59.2 billion, according to Gartner Inc., and is expected to reach $106.8 billion in 2022.

Growth in cloud spending accelerated during the pandemic, and is expected to help Amazon and Microsoft post another round of strong quarterly earnings when they report this week. Although multi-cloud arrangements might eat into some of the sales Amazon and Microsoft could land, in most cases they get at least a slice of customer spending.

Wall Street expects Amazon to report more than 30% year-over-year growth in cloud sales when it reports second-quarter results on Thursday. Microsoft's Azure cloud is expected to see more than 40% revenue growth when the software giant posts fourth-quarter earnings on Tuesday.

It isn't just corporate buyers rethinking their IT spending. When the Central Intelligence Agency began a major move to the cloud, it signed up with AWS in 2013. Last year, as the initial contract was coming to an end, the CIA said it opted for multiple vendors to take advantage of expanded cloud capabilities available by working with multiple providers.

This month the Pentagon scrapped plans to award a $10 billion, 10-year contract to Microsoft that was mired in controversy. The Pentagon said it would replace the contract, known as JEDI, with multiple awards.

John Sherman, the Pentagon's acting chief information officer, said JEDI was developed at a time when the department's needs were different "and our cloud conversancy less mature." Amazon and Microsoft would qualify to compete in the new round, and IBM, Oracle and Google also would be approached to potentially bid, he said. The Pentagon aims to award a contract in April.

Many companies have ended up with multiple clouds somewhat by chance, analysts and industry officials said. Different groups within an organization may have signed up with different vendors.

This year, 92% of companies had a multi-cloud strategy, up from 81% in 2018, according to an annual industry report published by software company Flexera Software LLC.

Operating across different service providers brings challenges, though. Each has its own way of handling the underlying technology, such as storage or networking, and moving data between clouds can be cumbersome, industry officials say.

USAA, the San Antonio-based insurance company, for years has been trying to work across cloud offerings in part to build resilience by being able to move data as needed, but it has found that challenging, said Michael Willette, assistant vice president responsible for cloud operations at USAA.

"Every cloud provider, even if they tell you they're not, is focusing on creating lock-in," he said.

That has spurred creation of a number of new software companies to provide tools to better manage applications across various clouds. One of the hottest cloud-service companies over the past two years has been Snowflake Inc., which helps companies manage their data across clouds. The stock soared when it went public last year, though it has come down from its highs late last year.

"Two and a half years ago, everything was AWS," said Steve Mullaney, chief executive officer of Aviatrix Systems Inc., a provider of networking software to help organizations to manage their clouds across multiple vendors. "Now everybody is multi-cloud."

The main cloud providers offer their own tools to allow customers to bridge systems. But many customers remain wary of their options because the cloud companies want to hold on to as much of the business as possible, industry officials say.

"You need an independent multi-cloud platform provider," said Dave McJannet, CEO of HashiCorp Inc., a provider of tools to work across clouds.

Google said it is using open-source technology that is free to adopt to give its customers more control over which cloud they use.

"Our customers don't want to rehash the same vendor lock-in playbook from the 1990s," said Eyal Manor, a vice president at Google Cloud.

Microsoft said it is working with customers to address their cloud needs, including those spanning other vendors. An Amazon spokesman said most customers, even those that talk about using several providers, stick with one.

The Pentagon, meanwhile, is already looking down the road with plans for another big cloud competition in early 2025.

Write to Aaron Tilley at aaron.tilley@wsj.com