I've been reading about modernist cuisine recently and the prospect of clarifying juices with agar gellification. Gelatin clarification has been a thing for awhile, but it has some side effects that are theoretically absent from agar clarification. Basically what you do is add the agar powder (an extract from a seaweed) to your liquid and then cool it off so that it sets as a gel. Then when you place this over a sieve with some cheesecloth (I used a cloth napkin) and it'll cause the gel to weep out the liquid. This clarifies the drink by trapping the undissolved solids in the gel while releasing the dissolved solids with the liquid.
http://www.cookingissues.com/index.html%3Fp=1439.html is the article I used
it was a bit too tedious to do for a single drink, but I could see doing it in larger quantities. It had a definite impact on the flavor of the coffee. I think if I had a better filter than just a cloth napkin it would be any better because I think some flavor from the cloth ended up coming through. But the flavor of the coffee was definitely enhanced, both for better and worse.
One of the downsides of french press IMO is that it often tastes really muddied, which is also kind of the appeal. So it was pretty cool how the clarified product helped unmuddy those flavors so you could better detect the individual compounds.