Hmm. I think the opposite would be more useful.

Think Danbooru style, where you can give a thread "tags" instead of posting on a specific board. Maybe a new thread would be posted "onto" a specific board, /ck/ for example, and as people replied they could add new board-tags to the thread, say one new board tag per post. And maybe one of the functions of a moderator/janitor would be to remove irrelevant tags from threads much like deleting the thread except it still exists on the board that it's actually related to.

If you did it that way you could look at multiple boards the way you're suggesting - just request the union of all the board-tags. But! You could also look up the intersection of tags to define precisely what you're actually interested in seeing. So if all you want is threads related to news about car-related television shows, you could go to 4chan.org/new/o/tv/. (And just think about what fun you might have if you wanted to see threads about flash animations of lesbians who cook!)