The studies commonly cited by authorities to claim vaccines are safe compare individuals who got one particular vaccine and dozens of others to those who got dozens of others. Such a study wouldn't show statistically significant damage unless the particular vaccine causes at least damage comparable by itself to the damage caused by all the other vaccines. But peer reviewed animal studies indicate that any vaccine causes damage if it occurs at the wrong time, and indicate that repeated vaccines cause autoimmune problems, and indicate the total aluminum load is a problem, and indicate that many vaccines may suffer from damaging contaminants. So there is considerable reason to suspect every one of them simultaneously.
All the epidemiological studies that compare individuals who got more vaccines to individuals who got less, either indicate that more is worse, or have gross methodological problems that invalidate them.