The challenge has been accepted, three consecutive studio albums released by artist or band. My top 20 list of consecutive releases. No live or greatest hits allowed.
The list of course is very subjective and is absent some major artists, and some remarkable albums. No Bob Dylan, Bruce Springsteen, Beach Boys, Grateful Dead or Van Halen. No Santana, Paul McCartney, Police, Tom Petty or AC/DC. No mixing of group and solo albums. Sometimes two classic albums were grouped with a less successful album (or simply one I don’t like), so that that artist did not make list.
The Beatles: Rubber Soul (1965), Revolver (1966), Sgt. Pepper’s Lonely Hearts Club Band (1967)
Yes: The Yes Album (1971), Fragile (1972), Close to the Edge (1972)
The Moody Blues: In Search of the Lost Chord (1968), On the Threshold of a Dream (1969), To Our Children’s, Children’s Children (1969)
The Who: Tommy (1969), Who’s Next (1971), Quadrophenia (1973)
Led Zeppelin: Led Zeppelin (1969), Led Zeppelin II (1969), Led Zeppelin III (1970)
Steely Dan: The Royal Scam (1976), Aja (1977), Gaucho (1980)
David Bowie: Diamond Dogs (1974), Young Americans (1975), Station to Station (1976)
Neil Young: Everybody Knows This is Nowhere (1969), After the Gold Rush (1970), Harvest (1972)
The Kinks: Low Budget (1979), Give the People What They Want (1981), State of Confusion (1983)
The Rolling Stones: Sticky Fingers (1971), Exile on Main Street (1972), Goat Head Soup (1973)
Elvis Costello: This Year’s Model (1978), Armed Forces (1979), Get Happy! (1980)
Electric Light Orchestra: Face the Music (1975), New World Record (1976), Out of the Blue (1977)
Jethro Tull: Stand Up (1969), Benefit (1970), Aqualung (1971)
Alice Cooper Group: Killer (1971), School’s Out (1972), Billion Dollar Babies (1973)
Joni Mitchell: Court and Spark (1975), The Hissing of Summer Lawns (1975), Hejira (1976)
Simon & Garfunkel: Parsley, Sage, Rosemary and Thyme (1966), Bookends (1968), Bridge Over Troubled Water (1970)
Jeff Beck: Blow By Blow (1975), Wired (1976), There and Back (1980)
Doobie Brothers: The Captain and Me (1973), What Were Once Vices Are Now Habits (1974), Stampede (1975)
Elton John: Honky Château (1972), Don’t Shoot Me I’m Only the Piano Player (1973), Goodbye Yellow Brick Road (1973)
Hall and Oates: Private Eyes (1981), H2O (1983), Big Bam Boom (1984)
Bonus:
Allman Brothers Band: Idlewild South (1970), Eat a Peach (1972), Brothers and Sisters (1973)
Stevie Wonder: Innervisions (1973), Fulfillingness’ First Finale (1974), Songs in the Key of Life (1976)
Chicago: Chicago Transit Authority (1969), Chicago (1970), Chicago III (1971)
Billy Joel: 52nd Street (1978), Glass Houses (1980), The Nylon Curtain (1981)
Ticket 2 Ride 
To a ranking-challenged individual who also easily falls into the trap of overthinking stuff, your exercise sounds terrifying! 🙂
That said, I think your list looks great. Shockingly, without having given it much thought, some of my tweaks to your list would be the following:
The Beatles: Sgt. Pepper’s Lonely Hearts Club Band (1967), Magical Mystery Tour (1967); The Beatles (1968)
Led Zeppelin: Led Zeppelin II (1969), Led Zeppelin III (1970), Led Zeppelin IV (1971)
Steely Dan: Katy Lied (1975), The Royal Scam (1976), Aja (1977)
David Bowie: Hunky Dory (1971), The Rise and Fall of Ziggy Stardust and the Spiders from Mars (1972), Alladin Sane (1973)
Kinks: Kinks (1964), Kinda Kinks (1965), The Kink Kontroversy (1965)
In addition, I would add Pink Floyd to the list:
Pink Floyd: The Dark of the Moon (1973), Wish You Were Here (1975), Animals (1977)
If I had to remove one band or artist to accommodate Floyd, I would go with Alice Cooper, though I do like him as well in general.
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I almost included Pink Floyd, but I’m not much of an Animals fan.
Your selections are solid.
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