I had to think quite hard about this one - I kept thinking of artists with loads of great albums and then getting hung up because they didn't have four consecutive good ones. For example, like the OP, I wanted to say Metallica, but while Kill 'Em All, Ride the Lightning and Master of Puppets are absolute thrash classics, unfortunately I am of the opinion that ...And Justice for All is badly-mixed, boring and generally pants. Anyway, I did come up with some:
Iron Maiden - Piece of Mind, Powerslave, Somewhere in Time, Seventh Son of a Seventh Son.
I was tempted to say that all of the first 7 of Iron Maiden's albums were great, and while I do enjoy them, I think The Number of the Beast is the weak link in the chain, so it's these four, starting from album 4 through to 7. Piece of Mind and Powerslave are awesome heavy metal albums, easily some of the best out of there, while Somewhere in Time and Seventh Son are the best showcases of Maiden's experiments with prog.
In Flames - The Jester Race, Whoracle, Clayman, Colony (plus Lunar Strain right at the start for a string of 5 albums)
Aside from the fact that all of the first 5 albums were totally instrumental in the creation of melodic death metal (as well as folk metal with Lunar Strain), it wasn't until The Jester Race that In Flames really got the power and energy of death metal into their songs, before the next three albums added in some unbeatable melody work.
Amon Amarth - not even going to lie, every one of their albums is pure gold. But, the four I'd pick are: Fate of Norns, With Oden On Our Side, Twilight of the Thunder God, Surtur Rising (bear in mind I've not listened to Deceiver of the Gods yet, but I'm sure it'll be as brilliant as the rest)
Amon Amarth have never made a bad album. Every single one is a masterclass in how to write death metal, and they only get crisper, clearer and tighter with each release.
Rise Against - Siren Song of the Counter Culture, The Sufferer and the Witness, Appeal to Reason, Endgame
Again, another band I love everything they've produced, and again, it's the latest four albums because they get better and better each time.