Can having multiple vaccinations actually lead to a weaker immune system?

Probably not: If anything, it should stimulate ones immune system.

No: Actual testing shows the present system of multiple separate vaccines (even 6) at the same visit are both safe and effective. The immune challenge of such an encounter is actually less than a single smallpox inoculation as it was given routinely up until 1980.The idea of spreading these promoted by ex Playboy bunnies and a few physicians has no benefit based in fact or research.