The nation’s largest pension funds and other institutional investors want the Securities and Exchange Commission to make listed companies provide more information on their so-called “human capital.”

Improved transparency on issues such as workforce diversity, pay practices and corporate culture could help investors see which companies carry a competitive advantage and which ones face reputational or legal risks. But “human capital is nearly invisible in the commission’s disclosure rules,” the group of investors with more than $2.8 trillion in assets...