I find that often times, games play very differently depending on the number of players, so it makes sense to have separate ELO ratings for each player count. In terms of implementation, it may be a bit tricky to have separate ratings for each player count. For example, if you're screening players based on ratings, which ratings is used? In addition to variants based on the number of players, there are also rule variants. The rule variants can also change gameplay strategy as well, but I don't think it's realistic to have too much granularity in the ratings. The list below only considers player variants.
Variants, Players, Games
(4) 2-5 Hawaii, Puerto Rico, In the Year of the Dragon
(3) 2-4 Stone Age, Dominion, Race, Can't Stop, Troyes, Gosu, Amyitis, Tobago, Uncle Chestnut's Table Gype
(3) 3-5 Coloretto
(2) 2-3 Haggis
(1) 2 Kahuna, Dragonheart, China Gold