In all games, Hit points & Experience points increase with more players in game (+50% of the base, for each new player).
In all games, number of drops tend to increase (a stat called "NoDrop" and associated to each Treasure Class decreases), though the effect is much more noticable when the number of drops was initially low (ie : normal monsters).
In Ladder and SP nightmare & hell games, base damage and poison length increases (+6.25% of the base) for each new player in game. No such thing happens to attack rating, however.
Indeed, Corpse Explosion doesn't scale the new amount of HP of monsters. That's why only 1 CE is enough in solo games to get rid off huge packs of monsters, whereas you need to cast it several times in full games for the same effect.
The same happens for Crushing blow.
Fortunately, the same happens also for hostile Death damage (from dolls or suicide minions) and Nihlathak's Corpse explosion
On the contrary, Static shield has its effect calculated according to the current life of monsters. It's by far the #1 skill to use in full games.