Some years ago, I handled a sizable case regarding the applicability and enforceability of an anti-stacking provision.
The policy had two main liability coverage parts, general and professional liability, each with its own sizable limit. It was somewhat specialized to the specific industry of the insured. As such, the CGL part included certain civil rights claims. Such claims were not necessarily mutually exclusive with the professional liability coverages. There was an anti-stacking endorsement which was presumably added to avoid a single claim being able to touch both the CGL and PL limits.
In my case, there was such a claim. Moreover, it was argued that there were acts giving rise to the injury that occurred just before and after the policy renewal date. Thus, it was argued that injury tapped up to four policy limits (2 coverages x 2 policy years)!
After significant litigation, the court was not satisfied with the language in the anti-stacking endorsement and held that multiple limits were in play.