The Vaccine Information Sheets on the CDC's own website are also very telling. For instance, re the MMR vaccine the CDC advises: "Some people who are sick at the time the shot is scheduled may be advised to wait until they recover before getting MMR vaccine." To me, this supports the theory that your immune system can literally get overwhelmed - already sick and adding 4 viruses (probably more that day if you are following recommended schedule) isnt' a good idea.
CDC also says:
"Tell your doctor if the person getting the vaccine: Has ...another disease that affects the immune system
Is being treated with drugs that affect the immune system...
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Has gotten another vaccine within the past 4 weeks
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Any of these might be a reason to not get the vaccine, or delay vaccination until later."
Again, to me they are acknowleding that you don't kick a man while he's down, ie don't overload the immune system when it's already workign overtime.
Finally, I look at the warnings that are printed right on the vaccine information sheets including:
"Several other severe problems have been reported after a child gets MMR vaccine, including: Long-term seizures, coma, or lowered consciousness
Permanent brain damage"