On the veterinary side, combo vaccinations have to be tested for lack of interference, and sometimes there is interference, meaning the response to an antigen in a combo vaccine is less than when administered alone. So it’s not so simple. Also, the type of vaccine, adjuvant (or not) used, and type of antigen all affect vaccine efficacy.

By the same token, we are bombarded by infectious agents, especially when the little ones start going to daycare. The immune system can certainly handle this. Administering a vaccine is different though, for many reasons, including that the antigen is often presented differently than with an actual infection. Think adjuvanted killed influenza virus vaccine administered intramuscularly.