How do you handle systems accessing multiple components (without dropping your cache load) in an entity component system?

Question

I'm currently writing my own Entity Component System, and I'm having a little bit of trouble optimizing my cache load when it comes to systems that look at multiple components.

I'm taking a very pure ECS approach: components of the same type are stored in a (sparse) vector, and entities are identified by their index in each component vector. I understand that this is good for performance, because a system working on a single component can fill the cache load fully with components that it needs.

But an issue arises when a system uses multiple components, and I don't know what I'm missing; for each entity, a system will need to drop its cache load of one component to look at the next one. Each component type a system looks at means a cache drop for each entity it looks at.

Is my problem clear? Does anyone have any solutions to this? What am I missing?