The answer to this is Yes and No.
When we are developing inside our own mothers, as mammals, we develop what’s known as a milk line that extends from the underarms to the groin. This is obvious in other mammals who have multiple nipples. This occurs along these lines in all mammals, many with multiple pairs. According to the 2015 edition of Guinness World Records, the female shrewish short-tailed opossum holds the record at 27!
In humans, however, as we develop, the extra breast tissue along the milk line disappears and we are left with just a pair of nipples, one on each side.
Interestingly, extra nipples are more common in men, where they are usually quite small, and are often mistaken for a mole. Areolas may develop around the nipple, or not. I often find an extra nipple on patients during a routine exam, and most of the time, they look like a mole. Rarely, will there be enough breast tissue underneath this extra nipple to swell or grow.
It is rare that extra breast tissue or nipple is a cause for medical concern. Many women and men do elect to have them removed for cosmetic reasons. The extra or “supernumerary” nipple can usually be excised with minimally invasive outpatient surgery. This may, or may not be covered by insurance.