The top four happens to be just the right amount for me, because there are exactly 4 albums that I know that I consider perfect 10's!
A lot of mine are very commonly praised albums, so I'm not going to waste my time talking about why I love Hospice/ITAOTS/Funeral/Kid A/etc. I'm sure you've heard about them a million times and there's nothing I can say that hasn't already been said However, I will talk about the top 5 very highly rated ("Second tier classic" or above) albums that I feel are underrated and overlooked.
Best songs - Somewhat Damaged, The Fragile, The Great Below
I've never understood why this album is considered to be one of Radiohead's weakest releases. In fact, I have a good friend who knows the entire Radiohead catalogue and considers this to be his favorite album of theirs! (Paging /u/inquisitiveiguana - maybe he can back me up) Although I personally wouldn't go that far, I still think The King of Limbs is an amazing album and completely undeserving of the disdain it gets among Radiohead fans. The twitchy loops and samples give the album (the 1st half at least) a very unique, claustrophobic feel, one I've truly never seen replicated somewhere else.
If you've heard this album and don't love it as much as me I fully understand why, but consider giving it another chance - its a slow grower that's well worth the time investment.
Best songs - Give Up the Ghost, Codex, Separator
This album isn't underrated really, it's nearly universally loved by everyone who knows it, but I'm just surprised how rarely it seems to come up in forums such as this one. I've never ever heard a single legitimate review denouncing how incredible this album is from start to finish, and I genuinely believe it's one of the greatest albums ever recorded. It's the type of album I could go on about all day - the production is flawless, the layered atmospheres and soundscapes created on songs like Mr. Self Destruct and Reptile are terrifyingly beautiful. The lyrics are visceral, raw and real - detailing a deeply flawed man and his destruction and eventual suicide. The track sequencing is perfect, all the songs come together perfectly to form a flawless concept album and not a single one is a weak link - the last 5 songs specifically pack an emotional punch that has nearly never been matched for me on another album. If you haven't listened to this album I implore you to, I guarantee you won't regret it.
Best songs - ALL OF THEM
Best songs - Where You'll Find Me Now, Gardenhead/Leave Me Alone, April 8th
Best songs - Company Calls Epilogue, No Joy In Mudville, Scientist Studies
And