In late April, when Mike Massaro set out to get $40 million to $75 million in funding for his payments start-up, Flywire, he contacted a small group of investors he already knew. But word quickly got around, and other investors flooded his inbox with $200 million of investment offers, half of which he turned down.

Gusto, a payroll and benefits software company, raised $140 million in July, but could have done five times that, according to Joshua Reeves, its chief executive and founder.

Convene, a real estate services start-up, recently obtained $152 million and turned away more than $100 million of additional investment. Soon after, another wave of hopeful investors called, asking if the company would be looking for more financing, according to Ryan Simonetti, Convene's chief executive.

Start-ups raising $100 million or more from investors — known as a mega-round in Silicon Valley — used to be a rarity. But now, they are practically routine, producing a frenzy around tech companies with enough scale and momentum to absorb a large check.

The jump in oversize investments is led by relatively new investors, including the Japanese conglomerate SoftBank, Chinese companies and sovereign wealth funds. They see a chance to capitalize on tech's incursion into just about every industry, and want to put their money down before the young companies go public.

By entering the tech market, they have all but eliminated talk in Silicon Valley about an investment bubble — a leading concern a couple of years ago — because the money now seems almost limitless.

For the start-ups, the pots of money are changing the normal way of building a tech company. They must move even faster, expand their ambitions and collect more investment money than ever — even if they might not be ready. They risk becoming too reliant on funding and never finding a path to profit.

"If your competitor is going to raise $150 million and you want to be conservative and only raise $20 million, you're going to get run over," said Bill Gurley, a managing partner at Benchmark Capital.

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Investors participated in a record 273 mega-rounds last year, according to the data provider Crunchbase. This year is on pace to easily eclipse that, with 268 completed in the first seven months of the year. In July, start-ups reached more than 50 financing deals worth a combined $15 billion, a new monthly high.

In the last 10 days, Letgo, an online classifieds ads company, raised $500 million. Actifio, a data storage company, took in $100 million. MyDreamPlus, a co-working space start-up, secured $120 million. And Klook, a travel activity booking site, got $200 million.

These mega-rounds have become so common that CB Insights, which tracks start-up investments, has even debated lifting its definition of a mega-round to $200 million or more, according to Anand Sanwal, the firm's chief executive.

Many of the new investors, including SoftBank's $93 billion Vision Fund, manage funds so large they dwarf the entire traditional venture capital market in the United States. These giant funds are looking for start-ups that can take large sums of money with one shot. Writing lots of small checks is too time-consuming, and the returns from small bets will not make a difference for a such a big fund. So investors are competing to back any start-up that shows promise and the ability to put $100 million or more to use.

"As soon as they feel like they have a winner, they will really put a lot of resources behind it," said Mr. Sanwal of CB Insights.

SoftBank's deal-making has affected every part of the venture capital market. The arrival of its Vision Fund, which has a minimum investment size of $100 million, has prompted a number of traditional venture capital firms, including Sequoia Capital, to build larger pools of money to compete. Funds from seven different firms are raising capital, according to the data provider Pitchbook.

But the Vision Fund is not even the most active mega-round investor. In the first seven months of 2018, Tencent Holdings participated in 31 rounds of funding of $100 million or more, compared with 18 for SoftBank, according to CB Insights. GIC and Temasek Holdings, investment funds associated with the government of Singapore, as well as Alibaba and Sequoia Capital China, have also been among the most active mega-round investors this year.

As a result, early investors must make sure their portfolio companies are friendly with the large funds, laying groundwork for a potential investment in the future.

"It feels like there is a bit of a beauty pageant that early-stage investors put on for the mega-funds," said Patricia Nakache, a general partner at Trinity Ventures.

The hot funding market is pushing high-growth start-ups to change their plans. Flywire was not going to pursue more investment money until next year. It still had $15 million in the bank from a previous funding round. But the company saw "investment heat" in the payments industry and Mr. Massaro thought more money would help Flywire grow even faster.

Funding rounds can take as long as six months to put together, but Flywire's round wrapped up in just over two. As a result of the capital, the company will complete some of its hiring plans in half the time it previously planned and expand into a new geographic market two years early.

Moving aggressively is not a choice. Well-funded start-ups, called "super-haves" by some investors, can afford to pay their employees more and lower their prices, losing money in the short term to win more customers.

Convene, the real estate start-up, competes tangentially with WeWork, an office rental company that has raised more than $8 billion in funding from SoftBank and other investors. Convene was not planning to chase more capital until later this year, but the company's investors encouraged it to move sooner. Business deals move faster today than they did five years ago, said Mr. Simonetti, the company's chief executive, and having extra capital on hand helps with speed.

"There's definitely a little bit of this, 'Let's overcapitalize the company a little bit so we can move quicker and faster,' " he said.

The large investors also demand big ideas from the start-ups. Softbank's Vision Fund team pushed Tina Sharkey, chief executive of e-commerce start-up Brandless, to share the most grandiose, ambitious version of her business road map.

"They were like, 'Come on, show us your real plan,' " she said. Brandless had barely been operating for a year before Ms. Sharkey outlined an expansive vision to use machine learning, data, curation, and community-building to create efficiencies. "We didn't have the gumption to say that to anyone else," she said. In July, SoftBank invested $224 million into her company.

"In today's hyper-connected world, companies need to hire, scale and enter new markets faster than ever before or risk being surpassed by others," said Jeff Housenbold, a managing partner at SoftBank Investment Advisers.

Few venture investors foresee a slowdown in the pace of mega-rounds. Those who once cautioned of a tech bubble and subsequent crash have given up on their warnings. In 2015, Mr. Gurley of Benchmark predicted "dead unicorns," referring to start-ups valued at $1 billion or more. But since 2015, the number of start-ups worth $1 billion or more has ballooned to 258 from 80, according to CB Insights. Excess funding is tied to inflated valuations, which may create problems when overvalued companies eventually try to go public.

Mr. Gurley said he was done trying to sound the alarm. "You have to adjust to the reality and play the game on the field," he said.

Annie Lamont, a managing partner at the venture fund Oak HC/FT, expected a drop-off in start-up valuations and funding three years ago, but it never happened. Now, she expects more of the same, partly because most the companies can easily get more money and few are worried about a downturn.

"The fear of a correction is not occurring," she said. If any start-ups do "vaporize," she said, "I think people are going to ignore them and roll right on to the next one."

Mitchell Green, a managing partner at Lead Edge Capital, does not imagine a slowdown unless interest rates increase significantly, a change that could prompt investors to move money into tax-free bonds. "It ain't going to stop," he said. "There's too much money."

Mr. Reeves, of software start-up Gusto, acknowledged that founders who obtain outsize sums of capital can get caught up in a "growth at any cost" mentality. That is why he chose not to maximize his funding round despite the intense interest. "It's up to the founder to realize that's a distraction," he said. "Success is not having more money or a bigger team, but having more customers or revenue."

Mr. Reeves is staying cautious, even when few others seem worried about a bubble. "The most likely time to have some type of correction, or change, or realization of the cycle turning, is when you're not talking about it," he said.