Is it possibly someone with antisocial personality disorder also suffer from borderline personality disorder?

Not really.: They are very different. Antisocial people don't really care for others, use people for their own means, do not have sincere emotions. In Borderline personality, people actually might care too much and don't know what to do with their feelings (so will react very extreme to a breakup or with friends). It might appear to overlap (both can have problems with anger), but they are different.