The set up to play Dominion with more than 4 players requires more treasure and victory cards. Therefore you need to have two Dominion games that include treasure and victory cards (that is the base game and Intrigue) to make it work.
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The Set Up
You need both the Dominion base set and Dominion Intrigue In the Intrigue rule book the set up is specified as follows:
To set up for 5 or 6 players, combine the Treasure cards from Dominion and Dominion: Intrigue. Use 15 Provinces in the Supply for a 5-player game and 18 Provinces in the Supply for a 6-player game. All other Victory card piles (Estates, Duchies, and Victory Kingdom cards) remain at 12 cards per pile. Use 40 Curse cards for a 5-player game and 50 Curse cards for a 6-player game.
In a 5 or 6 player game, the game ends at the end of any player’s turn when one of two conditions is met: the Supply pile of Province cards is empty OR any 4 Supply piles are empty.
Colonies
If you want to play Dominion Prosperity with more than 4 players, we recommend increasing the number of Colonies as well: 15 Colonies with 5 players and 18 Colonies with 6 players. This isn’t specified in the rules of Intrigue, but we think that’s only because Intrigue came out before Prosperity.
Dominion Prosperity comes with 12 Colonies only, so you can use blank cards to replace the lacking Colonies.
Game Length
Expansions
The only expansion that is strictly necessary to play Dominion with 5-6 players is Intrigue. The main expansion we would recommend to add is Prosperity, because it can shorten the game the most.
Other than that all expansions can work well with 5-6 players, so we recommend you look at our Dominion expansion ranking and find the one that appeals to you most.