Same way as always. Open the page, glance down it to see if there's anything that interests me, hit hide on the domains that I never want to see anything from. Lather, rinse, repeat.
But I'm guessing you have more of a FOMO (Fear Of Missing Out) kind of problem, which admittedly I don't have. However, you could look at something using RSS, maybe in combination with an agent told to find and show articles based on some heuristics.
Personally, I'm OK with missing something. If it's good, I figure it'll surface somewhere else and impinge on my notice sooner or later.