“Together there could be a possibility they are quite lethal. Separately it looks like they are not at all lethal, but just very effective.”

Oval Office remarks on signing the childhood vaccine executive order

The combined vaccine is safer than the diseases it prevents, and splitting it has no evidenced benefit. The Centers for Disease Control and Prevention states that getting the MMR vaccine is much safer than getting measles, mumps or rubella, and that no published scientific evidence shows any benefit in separating the combination vaccine into three individual shots. Two of his own appointees contradicted him: the administrator of the Centers for Medicare and Medicaid Services said the MMR vaccine is not a lethal vaccine, and his nominee to lead the Food and Drug Administration testified that it is not lethal and is safe and effective. The separate measles, mumps and rubella vaccines the order calls for are not licensed or approved in the United States.

Vaccination does carry rare severe risks, and that is the claim's best defence. The same CDC page records that severe allergic reactions following vaccination are rare but can be life threatening. That applies to vaccination generally rather than to combining the three components, which is what the claim turns on. The claim is also hedged, as a possibility rather than an assertion.