Thanks for your answer. Unfortunately cache dependencies do not address my scenario.
Cache dependencies allow you to control the output cache for content. It is also true, that content is cached per user. This must be the case, since I may be displaying the username or email address (for example) on my page. This is briefly mentioned in the docs and can also be verified by some simple testing.
So, cache dependencies are great if you are working in this "per-user" context. But I need to change that assumption, I need the cache to be maintained not just per user but per custom factor (in my case, a cookie). And all cache dependencies, whatever they are, can then be applied to this context.
So, I'm still looking for help here, as I don't see how this can be done.