Depends. The body creates antibodies towards more or less specific parts of surface molecules, the antigens. Now if your body manages to create antibodies that are found on both pathogens, they will both be subjected to the immune respone. There are antibodies more specific, so only a certain type of antigen can be adhered to, while other antibodies will attach to almost anything.

Now if person A develops antibodies that have a higher affinity to a antigen than person B, theirs will be more effective at binding pathogens. But there are so many more parameters to check that this alone is not enough to effectively fend off illnesses.

Yes, as some guys already mentioned: it's a new field, there is evidence, but no clear picture as to how far the manipulation/stimulation works.

Another keyword is "Extracellular Vesicles" that happened to be neglected in the body. Our cells and also bacteria secrete them, filled with a plethora of molecules of many many classes, which alter the body's response to stimuli.

Basically, what microorganisms have been doing to plants/other organisms, but now we know how and that it is happening similarly in us, too.