Can anyone have two privates

Technically, girls have two sets of private parts: their "bosom" and their "cooch."

However, I assume this question means "Can a person have both a "package" (male) and a "cooch" (female). The answer is yes. A fair amount of people are born with both sets of parts. These people are classified as one gender (the gender they choose or their chromosomal gender), but they really are both genders. People that are both male and female physically are called intersexindividuals. However, most intersex people choose one gender and stick with that one.