Sure. Here are two examples.
1. You're a web app company that routinely comes under DDOS attacks. A private security company would like you to subscribe and push Netflow traces to them during attacks, so they can derive minimal ACLs and relay them to ISPs so the attack could be filtered upstream. That Netflow data could in theory contain some of your traffic, and further could be statistically de-anonymized to reveal your personal usage of that service. Currently, you need authorization from your counsel every time you share that Netflow data; post-CISPA, you could get a one-time authorization and automatically push Netflow to the anti-DDOS provider.
2. You're working with several social networking companies to track down a browser malware attack that transmit itself through online messages. You'd like to collect a large volume of samples programmatically to share with other providers and LEOs, but you're extremely concerned that in doing so you might reveal details about private messages, perhaps even by sharing which users have messaging relationships with other users. Pre-CISPA, your counsel might refuse that sharing outright; post-CISPA, you'd have statutory protections for sharing that operational data in the course of responding to malware.