There are US states that are very deep into multi-stream recycling with 5 or 6 different bins. (Most of them are on the West Coast.)
There's an interesting debate on single-stream versus multi-stream recycling and its perverse incentives. Multi-stream recycling is more labor efficient, so in some cases more profitable, pushing labor to the unpaid consumer so that fewer laborers are needed at the recycling plants. Multi-stream recycling is often less efficient at overall recycling. Improperly sorted items are more likely to end up in landfills when the specialized recycling plant is an entirely different company with its own delivery schedule and process, versus a single-stream company that has to sort everything anyway.
In a somewhat surprising twist, some of the most efficient recyclers are the landfill companies themselves. Landfills take up space and don't produce income on their own. Finding any things that are recyclable and resellable is sometimes big profit. Sorting work is thus incentivized as profit growth. There are cities investigating going truly "single stream" again for all trash and continuing to incentivize the landfill companies to grow their recycling sorting processes.
Not only is that itself an illustration that companies need to be incentivized to do the right thing more than people need to be incentivized to do extra labor that result in less efficient outcomes, but it is also another example of how certain corporation's propaganda pushed the narrative from corporate action to consumer action.
The original lesson plan in the 1990s designed by some smart teachers was the Three R's: Reduce, Reuse, Recycle. They were put in this order specifically because they are in order of importance. Debates on if we are doing enough our own individual parts for Recycling have already lost the battle on how much corporations are helping us to Reuse things rather than recycle them, and better yet, to Reduce the number of things we need to even consider reusing or recycling or trashing. Both reduce and reuse require more collective action. They require companies to work outside of the "single use" box. Single use is more profitable, because it sells more single use things.