I would follow Phish (good luck, brave soul!) but I don't know the other two, so I guess that makes them each a Maybe.
Phish currently has 17 traditional studio albums, 2 traditional live albums, 3 live-only albums of original material, two non-official studio albums, and of course, the band has released dozens and dozens of other full show live releases, sound check jams, secret sets, every one of their shows from the last 19 years is officially released on the band's websites, and recordings in various quality of roughly 90% of all the shows they played from the 80s and 90s easily circulate for free to download online.
Considering they are known as a live band, and since many of their songs can only be found in live performances, I thought about going through the studio albums, with a corresponding live album/show every few releases that best represents the time period, but also includes as many live-only compositions as possible. I wouldn't start that until we got up to the band's first official live album, which was released after the band's 5th album. I would find it interesting as I haven't listened to the band's studio efforts in many years.
The Tangent are similar in some ways to The Flower Kings, proggy, hard, heavy riffs, mixed with loud synths but they have a jazzier edge and British vocals, not unlike Canterbury scene like The Soft Machine or Caravan.
Gateway was the jazz trio band of John Abercrombie, Dave Holland, and Jack DeJohnette. Technically they have only 4 albums, but the trio appears on 3 other albums so that beefs it up to 7 albums. So that wouldn't be the longest discography thread.