On Yakima's website there is discussion of this. There are a some models that handle 4 bikes. The FAQ's for these (eg for the Ridgeback 4) discuss the class of receiver you need (under some conditions only class 1, apparently). There are also downloadable instructions that might say more.

Keep in mind that 4 heavy bikes (40lbs each?) and a 35 to 40lbs rack is 195-200lbs. Maybe use class II to be safe, but I'd be surprised if Class 3 was needed.