Antisocial personality disorder is another name for secondary psychopathy and/or sociopathy. I believe it was Kraeplin who introduced the distinction between the primary psychopath and the secondary psychopath. The secondary psychopath is a product of the environment. The cause of primary psychopathy is idiopathic (i.e. nature). That's actually one of the problems with Antisocial Personality Disorder in the DSM as pointed out by Robert Hare and others. People who are very different can be diagnosed with it because there's hundreds of different environmental influences that can produce it. ASPD is merely behavioral in nature. So yes, any NPA type can develop ASPD.
This is why Robert Hare came up with the psychopathy checklist because he thought there needed to be an interpersonal dimension to psychopathy besides a pattern of irresponsible and risky behavior.