Mr. Woods has taken several steps to shake up Exxon's insularity, embrace new risks and jettison less profitable areas. People familiar with the matter said Exxon is weighing reducing its exposure to Canada, where it has operated for 130 years. Getting oil from Canada's oil sands is expensive, and the prospect of reduced exposure has signaled to some advisers that the company may become more aggressive in seeking transformation.
The company is also developing a more robust trading operation with an eye toward using regional oil and gas price disparities in the U.S. and around the world to boost profits, according to people familiar with the process.
Still, the centerpiece of Mr. Woods's turnaround effort is a major increase in spending, much of which is focused on drilling in Brazil, Papua New Guinea, Mozambique and Texas. In March, he said such opportunities are the best Exxon has seen since its merger with Mobil. They will make it possible for the company to produce an additional one million barrels of oil and gas a day, he said. Combined with existing production, that would equate to five million daily barrels, a record for Exxon.
Next year, Exxon is set to spend $28 billion, 45% more than in 2016. That's a marked difference from rivals such as Chevron, which is holding investment levels flat this year and 18% below 2016 levels.
Shareholders haven't responded with enthusiasm. The price of crude is up about 60% in the past year, but Exxon shares are up less than 5%.
Earlier in the year, analyst Paul Sankey, then of Wolfe Research, said clients were calling for an activist investor to force the company to take more "radical action." The unrest has calmed somewhat with oil's rally, analysts say. But shareholders are still looking for big change.
"Darren Woods is turning the Exxon Mobil supertanker, but the scale of the challenge is giant," said Mr. Sankey, now an analyst at Mizuho Energy. Exxon is poised to rebound in three to five years, but other companies are better bets for now, he said.
Investors are favoring smaller, nimbler competitors. ConocoPhillips, which has seen its shares rise 60% since last year, shed a number of businesses and promised to distribute much of its excess cash to shareholders in coming years rather than reinvesting.
From January to March, EOG Resources Inc., the biggest American shale producer, reported higher per-share profits than Exxon, a company five times its size. EOG's stock is up 84% in the last five years. Exxon is down about 10% in that time.
Meanwhile, rivals such as Shell, BP and Total have diversified outside of fossil fuels.
"Through the ups and downs of oil prices, Exxon always had very high returns, but that has changed," said Jonathan Waghorn, a portfolio manager at Guinness Atkinson Management Inc. It sold out of its Exxon position last year.
--Alison Sider contributed to this article.
Write to Bradley Olson at Bradley.Olson@wsj.com
Corrections & Amplifications The chart on oil and gas production is in millions of barrels a day. An earlier version of this article incorrectly stated in the chart that production was in billions of barrels a day. (July 13, 2018)