BOSTON (Reuters) - U.S. public pension funds normally prefer a backseat role in overseeing the future of companies where they have billions of dollars invested. But a new effort by New York City Comptroller Scott Stringer could show how public sector finance officials might become more involved by putting forward their own candidates for boards of directors. It could also mean another shake-up for corporations still learning how to deal with election contests brought by big activist investors like Carl Icahn or Nelson Peltz.     With New York City having the fourth-largest U.S. public pension system with some $170 billion in assets, Stringer has led the charge on bylaw changes known as “proxy access” under which hundreds of U.S. companies have made it easier for groups of shareholders to run their own candidates for corporate boards.  Now aides to Stringer say they may take their efforts another step and start suggesting specific board candidates at companies whose shares New York City pension funds own — which could include nearly any firm in the S&P 500. Goals would include making boardrooms more diverse or accountable for poor performance. While the comptroller’s office still prefers quiet talks, the new rules will give activists more leverage in those rare cases when corporate directors will not budge, said Michael Garland, an assistant comptroller. “We’re committed to being able to have a discussion about a particular nominee. We have the firepower to do that,” Garland said in a telephone interview on Wednesday. Garland and Rhonda Brauer, recently named as Stringer’s director of corporate engagement, declined to name any companies where they might suggest such nominations soon. By Stringer’s count more than 300 U.S. companies, including about half the S&P 500, have adopted rules to open up the nominating process, including Apple Inc (AAPL.O) and Exxon Mobil Corp (XOM.N). Exxon is under pressure to add a climate expert to the oil company’s board.     Still, even talk of specific directors brings the New York City funds into new territory as other big public pension managers have preferred a secondary role.  The California Public Employees’ Retirement System, the nation’s largest public pension system, and the Florida State Board of Administration have been vocal about issues like board diversity and voting rights but representatives of each said they are not currently pursuing nominations.  According to a December study by FactSet, companies won board seat proxy contests 67 percent of the time in 2016, up from 54 percent in 2015.  Jill Fisch, a University of Pennsylvania law professor who follows corporate governance, said investors have wondered if pension funds might use proxy access like big hedge funds to push their own candidates - and if so, whether their nominees would be successful. “I can imagine that being really effective, or a real disaster,” she said.     