Individual investors have found their next short-squeeze target in little-known software company Support.com Inc.

Shares of the company have more than tripled in the past week, pushing the stock to finish Monday at $36.39. That gives Support.com, a technical- and customer-support provider, a 38% gain for the day and a more than 1,500% jump for the year.

Some retail traders are piling into Support.com, scooping up shares and placing bullish wagers on the stock. One of the reasons why: Support.com has elevated interest from bearish investors known as short sellers. Investors on social-media platforms have recently discussed the potential for setting up a short squeeze.

Short sellers are investors who bet against a company by borrowing shares and selling them, hoping they can buy them back later at a lower price. But these short sellers can be burned by such wagers when the stock rises. They are then forced to buy back stock to try to limit their losses. Buying more stock can put further pressure on the stock price in what is known as a short squeeze.

This year, individual investors have crowded into companies with elevated levels of short-selling activity, as part of a larger strategy to reap big gains and turn upside down a market that many say has long been stacked against them. More than 20 million new retail brokerage accounts are estimated to have been created since the start of 2020, according to JMP Securities. Most notably, individual investors have tried to force short squeezes in companies including GameStop Corp. and AMC Entertainment Holdings Inc. this year. They have also driven higher stocks ranging from car-rental company Hertz Global Holdings Inc. to laser-scanning technology firm MicroVision Inc.

The recent run-up in Support.com shares marks a striking turnaround for the company, which started the year trading just above $2. The last time the company traded above Monday’s closing price of $36.39 was 2004. For the quarter ended June 30, the company reported total revenue of roughly $8.5 million and a net loss of nearly $800,000.

In March, Support.com announced a merger agreement with Greenidge Generation Holdings Inc., a bitcoin-mining company, in a deal that is expected to close this quarter. As part of the agreement, Support.com will become a wholly owned subsidiary of Greenidge, according to a news release issued at the time, Support.com is expected to provide Greenidge with an estimated $33 million of additional cash. Upon completion of the deal, Support.com stockholders and option holders will collectively own about 8% of the combined company’s common stock.

In mid-to-late August, short interest in Support.com has hovered around 60% of the stock’s free float, according to data from analytics firm S3 Partners. In the past week, a small degree of short-covering—or buying back shares—has occurred, data from S3 shows, with short interest declining by nearly 3 percentage points, or roughly 280,000 shares, between Monday and Friday of last week.

The volume of short-covering likely isn’t enough to move Support.com’s share price significantly higher, said Ihor Dusaniwsky, head of predictive analytics at S3, especially given the elevated trading volume that Support.com has recently experienced. Between Aug. 20 and Aug. 27, an average of 77.81 million Support.com shares changed hands each day, according to Dow Jones Market Data, versus an average trading volume of 3.98 million shares this year through the end of July.

As a result, Mr. Dusaniwsky said, much of the rally has been driven by share purchases and options activity.

“It’s momentum on the long side, where you get group, herd mentality into a name,” he said. Much of the recent activity has likely been driven by individual investors, he said, but he added that “good hedge funds don’t let high volatility situations go to waste.”

Retail investors purchased a net $38.1 million of Support.com stock in the week ended Friday, according to data from Vanda Research’s VandaTrack, making it the 15th-most purchased stock by individual investors for the week. Still, that buying activity was just a fraction of what other retail-investor favorites received. AMC attracted a net $192.2 million of inflows in the week ended Friday, while Nvidia Corp. received a net $136 million of buying during the same period, too.

As they have with many other short-squeeze targets this year, traders rushed to the options market to place wagers on Support.com’s stock. The jump in Support.com’s share price coincided with heavy options trading, with around triple the volume there typically is in the stock, according to Cboe Global Markets data.

Bullish call options tied to the shares jumping to $85 were among the most popular contracts changing hands on Monday. Calls confer the right to buy shares at certain prices, later in time. Other popular bets included put options tied to the shares falling to $15. Puts confer the right to sell shares.

At times, the heavy options activity in individual stocks has helped exacerbate rallies in the shares themselves.

—Gunjan Banerji contributed to this article.

Write to Caitlin McCabe at caitlin.mccabe@wsj.com