My current personal mechanistic model is that for "a given challenge" (that occurs in a window roughly 6-21 days large, with variation between people and also between challenges for the same person in different states of health), people either have a germinal center response, or not.
If not, then on a second attempt they might have a response again, or not. This is "in general". I've seen studies where they did really good followup with a population for a measles vaccine, and some patients managed to play along with followup 5 times, and only the 6th vaccine caused their immune system to finally begin testing positive for the desired antibodies.
However, my current personal mechanistic model has huge error bars, and numerous asterisks, with warnings about how immunology is a blacker art that computer security, because it basically IS computer security, but for programs written in nucleic acid that are billions of years old, with millions of new revisions spammed into existence every second by a mad god. I can't read the code (at least not most of it, and not easily). I just expect it to contain devilish tricks because: it would be surprising if it didn't.
Under the simple "response or not" model, the reason they did "two tries without bothering to check in between for a response" for the current Pfizer/Moderna design is that this "double tap" protocol ups the official "chance of having the response from the one official protocol" and basically jukes their numbers, so they can brag about a 90% efficacy "if you do it right" and this makes the narrative and the medical protocols and everything simpler.
If I was rich enough to have a private doctor (I'm not, and I don't even have "a doctor" as such because of moves and paperwork and dealing with insurance paperwork constantly being so so so exhausting) then I could totally see just paying "a one good doctors" to acquire and administer one vaccine dose, testing for response, then doing another dose only if the antibody test is negative... but also doing a third if the antibody test after the second didn't show that it worked, and so on.
However, under the "response or not" model this binary response is for a specific epitope (or epitopeS if several antibodies form for different surface bits of different proteins... I'm not personally clear on how the immune system picks exactly what folded protein surface part(s) to pick as a target, or why) and so if you have DIFFERENT vaccines that target DIFFERENT surface patches on the same set of proteins (or variants of proteins) then for a specific later challenge by an environmental exposure probably the best fitting antibody for that exposure reacts the strongest and leads charge by the immune system to fight off the invading virus particles and their initial first couple generations of viral babies.
My current working model might be wrong. If it is right, then the best vaccines would target lots of different epitopes selected from numerous possible genetic variants and we would generate and ship them in maybe close to realtime, as a sort of "human culture and institution mediated meta immune system".
This is how a properly designed public health system would actually work. But the US does not have a public health system basically? It just has a pharmaceutical and medical licensing monopoly maintenance and legal challenge immunization system, that prevents incumbents in the medical industry from being competed into low margins and high consumer health surpluses :-(
If our country was well run, we would already have a delta booster designed and available that could trigger the formation of these new kinds of antibodies, and the reason we don't is because the government is "either evil or incompetent" and the private industry isn't allowed to innovate around this barrier to technologically solving technologically solvable problems. ("FDA delenda est", but that's neither here not there.)
(Maaaaybe someone HAS already designed such boosters, but the FDA and/or CDC threatened them with angry looks and being put on some kind of professional blacklist if they ever admitted this in public on the second go-around because the PR was so bad for them when it came out that the first mRNA vaccine was designed in early 2020?)
Basically, my model is that RadVac or other novel vaccine designs COULD improve your response to VARIANTS by increasing the breadth of covid epitopes that your body can recognize and respond to, but that if a given vaccine design triggered a response in you already then another one is unlikely to help much more...
...however I have genuine model uncertainty. Maybe a second exposure causes the specific form of specific immune responses to somehow be stronger or different in a way that I've never seen a clean and clear explication of? Some anecdotal evidence suggests that double-dosed people are safer than single-dosed people, but I've never seen anyone report anything like this with a coherent followup about how or why such anecdotes might occur more (or less) in "different worlds" where (1) single-dosed people are less likely to have had a germinal response at all vs (2) the second dose materially changes the nature of the immune response.
I'm interested in learning a better model, if my model is wrong.
Another thing to point out is that having more antibodies is called "being allergic to things" when the thing you have antibodies for something that isn't actually bad. And it is called an "autoimmune disease" when the antibodies recognize something that naturally is already part of you. Acquiring new antibodies is not totally risk free. All biology is half black magic and full of exceptions because evolution is deep and twisty. Please please please be careful!
If you want to give me the $1000 for this writeup, please give it to johnswentworth instead.