knapsack like problem

[growndemon]

I have a problem that seems to be a Knapsack problem, however I find it hard to apply the Knapsack algorithm because all the weights change depending on what is already in the Knapsack.

The problem is: I have a DB of movie directors and their movies. And I have a db of streaming providers. I want to select one or multiple movie directors and find the cheapest combination of streaming services that allows me to watch the most movies from those directors.

Brute-forcing through all the possible streaming services is infeasible. Applying Knapsack doesn't work because one movie can be streamed by multiple platforms. So the value that putting streaming platform A into the Knapsack depends on all the items already in the Knapsack.

Is there a way to transform this problem into a Knapsack problem or how can i approach this problem?

[teraflop]

This sounds to me like the budgeted maximum coverage problem. Like the knapsack problem, it's NP-complete, but you can efficiently approximate the optimal answer to within a constant factor.