MSCI Inc., whose indexes guide the investment of about $11 trillion in assets, delayed a decision on whether companies that deprive public shareholders of voting rights should be barred from its benchmarks.

The company also broadened its investigation to consider “a discussion on the treatment of all types of unequal voting structures,” according to a statement Nov. 2.

Snap Inc., the parent of selfie app Snapchat, kicked up controversy earlier this year when the shares it sold in its initial...