Having multiple hobbies really help in dealing with this. One time you're doing this to death, then do the other thing to almost near death, then coming back to see the first one and enjoy it all over again. The only thing you might miss is the hype with fellow fans but that shouldn't be too big a problem, should it?
If you want more "depth" however, I think anime is not the best media to consider. Manga is somewhat better but I find that the medium that has deeper depth to it is the light novels and visual novels. Though even in these mediums, the diamonds are still hidden amidst the craps, similar with the anime. Though obviously there's the language barrier, but my LOVE of them destroyed that barrier by actually learning to read Japanese in autodidact.