SAN ANTONIO—Although large corporations can be lucrative clients for law firms they hire, a corporate client’s size can be a negative if the business owns several subsidiaries or affiliates.

In such instances, conflict of interest rules may preclude a firm from suing or opposing any of its client’s component entities. If the client’s corporate family tree is sprawling, experts say, a law firm will lose significant opportunities that could outweigh the value of the parent company’s business.

Law firms can...