The Dark Triad of personality, comprising Machiavellianism, narcissism, and psychopathy, was investigated in relation to the Supernumerary Personality Inventory (SPI) traits, because both sets of variables are predominantly distinct from the Big Five model of personality. Correlational and principal factor analyses were conducted to assess the relations between the Dark Triad and SPI traits. Multivariate behavioral genetic model-fitting analyses were also conducted to determine the correlated genetic and/or environmental underpinnings of the observed phenotypic correlations. Participants were 358 monozygotic and 98 same-sex dizygotic adult twin pairs from North America. As predicted, results revealed significant correlations between the Dark Triad and most SPI traits, and these correlations were primarily attributable to common genetic and non-shared environmental factors, except in the case of Machiavellianism, where shared environmental effects emerged. Three correlated factors were extracted during joint factor analysis of the Dark Triad and SPI traits, as well as a heritable general factor of personality — results that clarified the structure of the Dark Triad construct. It is concluded that the Dark Triad represents an exploitative and antisocial construct that extends beyond the Big Five model and shares a theoretical space with the SPI traits.