These three only have one even recognizable to the general public as a potentially dangerous condition. Due to mass media, TV and movies plots done by ignorant writers which exaggerate the psycho qualities of murderers for commercial success effects, the public is very misled about the worst dangers to them.
the three most dangerous mass murder types are:
(1) Anti-social Personality Disorder, or "sociopathy" in popular talk,
(2) Narcissistic Personality Disorder (not the popular concept of narcissism), and
(3) Paranoid Schizophrenic (the most recognizable delusional "crazy" the public knows about).
It is possible to have two or more mental disorders at the same time. Adam Lanza had a form of autism which led to him becoming anti-social. The anti-social disorder killed the kids, not the autism.
Sociopathy is extremely common, one lives in the nearest 13 houses to you. They do not all murder or mass murder, but being fundamentally anti-social, they break laws and hurt people in many ways because the like to. One in four girls is being molested before age 16 in one of those houses, or by a neighbor in one of those 13 houses.
Narcissistic Personality Disorder has many similarities but it is not the popular "ego-trip" idea of narcisssm. This person has a mental script they are acting out that makes them the star in "their movie" of their life. Given an abrupt shock to their worldview (spouse asks for divorce or boss fires them, or even somebody cuts them off in traffic, how dare they) and there is an explosion of violence we call "going postal". Familicides, murder-suicides, rampage killings often have this root cause.
Paranoids will hide their paranoia because, well, they are paranoid about how you will react to it.