The immune system does have a limit on the number of different pathogens it can remember and respond to at any one time, this concept is known as "immunological memory." However, the precise limit of how many pathogens the immune system can "remember" is not well understood and may vary from person to person. The immune system can handle a large number of different pathogens, but it's not unlimited.

When a person is vaccinated, the immune system is exposed to a small piece of the pathogen, such as a protein, rather than the actual pathogen itself. This allows the immune system to "learn" how to recognize and respond to that pathogen without causing an infection.

As a result, the immune system can develop "memory" of that pathogen, allowing it to respond more quickly and effectively if the person is exposed to the actual pathogen in the future.

It's worth noting that vaccines are developed for specific pathogens and it is not practical or necessary to make a vaccine for every pathogen that exists, as some of them are not dangerous to human health and many would not be able to be contracted by humans in the first place. Also, some pathogens are much harder to make vaccines for, for example, vaccines for viruses that frequently mutate like the flu.

The focus for vaccines development is usually on the pathogens that pose the greatest risk to public health, and the efforts are targeted on those that are most likely to cause severe illness or death, or that have the potential to spread easily in communities.