How many people can play in Euchre?
Wikipedia has rules for 8- and 9-person Euchre (along with a host of other variations), although we have to make some assumptions because the entries are missing some information. The entry for 8-person games:


  The players divide into four teams of two players. Teammates should be sitting directly across the table from each other (there should be three people between partners on either side). There will be 4 bowers, 1 right and 3 left.
  
  The rank of Trump goes as follows:
  
  
  Right Bower (jack of trump)
  1st played (left Bower) jack
  2nd played (left Bower) jack
  3rd played (left Bower) jack
  Ace, King, Queen, 10, 9.
  
  
  Scoring
  
  
  If a team calls trump and wins the hand (with 2, 3 or 4 tricks), they get 1  point.
  If a team calls trump and ties another team (each with 2 tricks), then both teams get 1 point.
  If a team calls trump and does not win the hand, the winner gets 2 points (if 2 other teams get two tricks they are both awarded 2 points).
  If a team takes all 5 tricks they receive 2 points (whether or not they called trump). If a person should choose to play the hand alone, they can get four points by taking 4 or 5 tricks.
  If they go alone and take less than 5 tricks, standard scoring applies.
  
  
  First team to get 10 points wins the game.


Given that the only ranks are A, K, Q, J, 10, and 9, this has to be played with two 24-card decks in order for there to be enough cards for 5 tricks (8 players X 5 tricks = 40 cards; this leaves 8 cards in the kitty). You'd also have to deal with duplicate cards played in the same hand. For example, a player leads of AH, which isn't trump, the next player also drops an AH, and miraculously everyone has to follow suit and no one plays a bower or trump card. Who gets the trick?

If nothing else, this variation changes the probability of getting a useless hand. If I'm fourth from the dealer, and my deal is 9H, 9C, 10C, QH, and KD, and someone in front of me calls Spades, I have no chance of taking a trick; there will always be someone who can play a bower or trump in five tricks. This problem also exists if you just expand the card pool down to include A through 3 (48 cards). As the card pool increases, the randomness also increases, leading to a higher chance for hands that can't win.