The body makes immunity by having immune cells like B cells which produce antibodies. Those lock onto the antigens of microorganisms that invade your body. There's a lot of complexity beyond that, but generally the limit is whether the microorganism has an antigen that fits an antibody your body has.

If it's fairly close, the body can use a partial fit to make more similar antibodies, so it doesn't need to be a perfect fit.

There's no hard limit that we could reach in a lifetime. Thanks to V(D)J recombination and Somatic hypermutation, there's a very high variance in possible combinations. It's just a matter of if you are lucky enough to have the right antibodies.

However, if you are repeatedly infected by something, it can occupy a large amount of your immune memory e.g. how most T cells in the elderly might be fighting HCMV antigens so it's complicated. Research is ongoing as to the limits of each factor.

One thing to consider in this train of thought is that those antibodies and cells are not being constantly produced or maintained. This is the beauty of “immunological memory”.

These cells die off in massive numbers once you clear a pathogen (or following vaccination), leaving behind a tiny colony of memory cells that lies relatively dormant until you encounter the same pathogen (or vaccinate antigen) again.

When that happens, they multiply enormously and mount a whole new immune response, then repeat. This is basically what allows an enormous & diverse immune library.

Using the computing analogy, it’s like running a program vs storing program files. You can’t run all your programs at once, but you can store a lot of program files.

There is obviously a lot more happening in the grand scheme of immunity but hope this is easier to understand!

One of the biggest issues with vaccines in general, is that the antibodies to some things just don’t stay in the body for very long. Some vaccines will work the rest of your life. Some will be gone in months.

The fact that viruses also mutate constantly, also make it necessary to create new vaccines constantly. That is why there is a new flu shot every year.

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.

Not possible for example one set of famous genes called HLA are inherited genetically and passed on through different ethnic groups. Human diversity alone and laws of inheritance mean some groups are more susceptible to diseases than others. Additionally, while capable (in theory) of creating antibodies against any foreign microorganism it never is 100% fullproof. Remember that microorganisms are not helpless against the mammalian body, they are much more effective at dampening immune response.

Interestingly there is a limit to the bloods ability to transport proteins and it’s viscosity. Too many cells make the blood too thick and too may proteins make the blood too thick. And having antibodies doesn’t work if you have like one molecule-there’s a minimum amount required to work. That said, I’ve never heard of someone maxing out via vaccines.

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As there is no limit on microorganisms as they seem to evolve, why should there be a limit on the amount of antidotes ? It just seems impossible, because we only know so little in the grand scope of things. Who knows what type of organisms are released from the ice.