“Now you have these attrition rates of like 20-plus percent,” he said. “How are you supposed to build an iconic legacy business when your entire employee base walks out the door every five years?”

Mr. Palihapitiya’s answer is to eliminate the I.P.O. process and its year and a half of “distractions trying to craft a bogus narrative,” as he described it, to entice investors. Instead, through his publicly traded vehicle, a unicorn company — shorthand for a $1 billion-plus private technology company — could reverse merge into it, instantly becoming public.

Unlike an initial public offering, in which employees and early investors all have certain “lockup” dates for when they can sell stock, he can write the rules however the company wants. Certain employees, for instance, could sell early, or the sales could be staggered so there isn’t an “overhang” on the stock that would depress the price before a major lockup period expired.

Mr. Palihapitiya also was able to choose most of the company’s big investors, who have agreed to their own lockups, making them much more oriented toward the long term. For all this, he takes a tidy fee: 20 percent of the $600 million. But if his company acquires a business five to 20 times its size through a reverse merger, he said, the fee is the same as or smaller than a banker’s fee — and it is all in stock, so unlike the banks, Mr. Palihapitiya’s interests are aligned with the company’s.

But Mr. Palihapitiya’s approach is just the tip of the iceberg. The most provocative plan floating around Silicon Valley is Mr. Ries’s LTSE. “It’s an intellectually thoughtful idea,” Mr. Palihapitiya said.

The idea, at its core, is to change the dynamic between the stock exchange and whom it serves, Mr. Ries explained, suggesting that traditional stock exchanges focus more on investors — and all associated trading revenue — than on the companies listed. That, he believes, leads to short-term thinking and trading.

Mr. Ries, who wrote a book titled “The Lean Startup,” is hoping to create an exchange that is focused on the needs of companies with a long-term vision and investors who are similarly aligned. He believes the problem facing private companies isn’t just the I.P.O. process but also “the lived experience of being a public company.”