Activist investors are like UPS drivers. They turn in only one direction.

By now, the activists’ rise is remarkable for its sheer scale and ferocity, with some $119 billion placed in their hands. Last year, they pursued 343 companies, up 27% from the year before, according to FactSet.

Their rise is also remarkable for another thing: their intellectual sameness. Plot a map of the 10 largest activist firms and you will find that seven of them are based within 17 blocks of each other in midtown Manhattan.

The vast majority are making similar demands of their targets, delivered with what now feels like a dull percussion: Raise the dividend, buy back shares, cut these costs, spin off that division, sell the company.

What’s the average length of an activist shareholding? Some 84% don’t last more than two years, according to FactSet.

Many of their grievances are built around the idea that companies are misallocating their capital. In this worldview, that capital is typically going toward bad long-term projects, such as AOL Inc. ’s ill-fated local news service Patch or the research budget at Allergan Inc. Many times they are right.

Here’s a drastic question for a field beset by conformity. Why can’t activists find targets where the misallocation is going the other way? In other words, identify companies that are playing it too safe, perhaps pushing too much into dividends or buybacks. Or missing a great opportunity in a new market.

Call it a radical mashup: The adversarial long-term investor.

“A company seems to be in a rut, and then an activist comes in and people get excited and they do things. And you have to wonder, why does it take that?” says Joseph M. Gingo, chairman of plastics company A. Schulman Inc., who helped turn it around with the help of Barington Capital Group, an activist that has been an investor in the company for nearly 10 years.

Think about how jarring it would be if Carl Icahn wrote a blistering letter to a management, demanding that it halt a buyback program and plow money into a promising new product. Or if another activist took out full-page ads insisting a company hire 200 more salespeople.

It just doesn’t happen. Consider the database kept by FactSet, which has tracked 3,774 activist campaigns since 2005, and has placed each in one of five categories. There is no such category for “advocating more long-term investment,” says FactSet vice president John Laide. “It’s an extremely rare demand, so we don’t code for it.”

This need not be so rare. These situations exist because by the laws of random distribution they must exist.There is more proof: These are the very opportunities that private-equity firms exploit, capitalizing on the market’s impatience for such undertakings.

Listen to Michael Dell , the entrepreneur who took his namesake company private in 2013. Here’s what he told the Council on Foreign Relations back in December: “You saw this pressure between the kind of short-term-minded investor and the long-term-minded investor, and so I felt the best option for the company to be able to invest more in R&D and get on a growth path once again and continue the strategy that we’re on, because we fundamentally haven’t changed the strategy since we’ve gone private. We’ve just accelerated it.”

I spoke to three leading activists about this idea and they surfaced three criticisms. One, it is human nature for CEOs to be biased toward overspending rather than underspending. Two, the idea of “deep activism” would require a set of investors comfortable with a far longer-time horizon than most activist-fund backers. Three, it could cause a destabilizing shareholder turnover, as, say, growth investors replace dividend clippers. “Yes, there’s something there,” one activist told me. “There’s just going to be a narrow set of companies.”

One person eager for such an approach is Ron Mock, the chief executive of the Ontario Teachers’ Pension Plan, a $141 billion fund looking to foster more long-term investing overall.

“I’d love to see that,” says Mr. Mock. “If you focused it on a long-term strategic approach, you’d find there are long-term investors out there.”

Mr. Mock’s views plug into a burgeoning movement across asset managers to push more long-term investing in the markets. They are, in fact, forming a new coalition called Focusing Capital on the Long-Term, and will meet in New York in March to press their agenda. The group includes fund manager BlackRock , insurer AXA , and Singapore’s sovereign wealth fund GIC.

All of this suggests opportunity awaits the intrepid activist who wants to differentiate himself. Call it the Deep Activism Fund and get fundraising. I’ll even write the pitch in proper Wall Street-ese:

“A fund that identifies and aggressively advocates for new approaches in companies suffering from chronic underinvestment and short-term management focus. Designed for patient investors who want to build real, sustainable value.”

—Email dennis.berman@wsj.com or Twitter @dkberman