Can someone with borderline personality disorder also have antisocial personality disorder?

Yes: These two personality disorders actually have some similarities and fall under the same group called cluster b personality disorders.

Traits: You may not have a diagnosable personality disorder. You can, however, exhibit traits from one or more personality disorders even if full criteria is not met for a diagnosis. You may also have a concurrent mental illness and a personality disorder. Many possibilities, only your psychologist or psychiatrist can positively diagnose you.