The chief executive officers of Bank of America Corp. and Johnson & Johnson have joined the leaders of 18 other firms and funds in backing an updated set of “commonsense” principles for U.S. corporate governance.

The principles now emphasize that publicly traded companies should get ahead of and respond to investor votes on executive pay, shareholder proposals, and other issues. There’s new language on board elections, including an endorsement of investors’ ability to nominate their own candidates.

The latest version...