There are growing attempts to remove plastics from the environment before it becomes micro plastic. But that's largely small scale projects as far as I've seen (generally localised surface netting contraptions). Whenever I've read about these projects, they're searching for funding to expand the reach of their projects. And it's not actually disposing of the plastic, just relocating it.
I don't see how we filter MP's from the environment once it's broken down that small. But there's research into bacteria that have evolved producing enzymes to use plastics as a food source.
I won't post the article as its massive. It's in the guardian so it won't be paywalled. But it's an interesting look at the discovery of the first bacteria in 2001 and the subsequent research into producing bacterial capable of producing plastic eating enzymes. Some of the most encouraging things I'll drop below.
A company called Carbios in France has developed a process that breaks down plastics to their components, ready to be remade into new more stable plastic than current recycling methods achieve (generally it's remade into less stable plastic than it would have been new with current methods).
The carbios process is expandable. They're moving to a facility capable of handling 130 tonnes a day, up from the 250kg it can handle daily at present. It's supposed to be about 51% more efficient than mining for and development of the component materials. And the main positive is it's using plastic already in existence more efficiently.
There is a lot of other research going on. But there is a massive amount of plastic in the environment. And most of the funding is focused on breaking it down into reusable components. There's still very limited work towards replicating the community of bacteria initially found at the dump which were breaking down the plastics into components while other microbes broke those components down further into nutrients. There's still plastics that can't be microbially broken down yet.
The positive I take from this is that nature itself had worked out the solution before we ever thought about it as a problem. Something out there will eat it if there's enough of it to eat. Nature's solution mightn't be quick enough to fix things. But it's giving us the tools to do so. If we can actually stop dumping the plastic we've made already and re use its components, at least it'll slow the build up and give nature a chance to work on what we can't pick up.