Eventbrite Inc., EVO Payments Inc., and other companies that use stock to help founders and other insiders keep control after going public are increasingly giving in to investors’ call for limits.

One-third of companies with a separate class of stock that gives insiders extra voting power compared to other shareholders have put an expiration date on that power, according to data from the Council of Institutional Investors for listings on U.S. exchanges so far this year. That’s up from 2017,...