There are several problems with the "too many vaccines, too soon" idea.
First, a study in the UK found that using modern criteria, the incidence of autism does not differ by much with age--up to age 70. This agrees with the scientific consensus that the apparent increase in autism is largely, probably entirely, due to increased diagnosis
Second, our immune system has evolved to deal with huge numbers of natural "vaccines" from bacteria and viruses constantly introduced through every scratch, scrape, and inflammation. And the number of antigens introduced from natural bacteria and viruses are far in excess of the simplified antigens that are introduced in vaccines. If you study that antibodies produced from even one infection, you find that the number of antibodies produced are easily in the excess of dozens.
So it simply does not make sense.