Three, four or more: what’s the magic number for booster shots?

Considering the flu shot is annual, "as many as necessary".

The booster will become a regularly changing shot.

Here the comment about variants as described in the original paper..

Vaccination before or after SARS-CoV-2 infection leads to robust humoral response and antibodies that effectively neutralize variants. This is because all the variants have common elements that are not expressed via the spike protein based RNA vaccine. Pfizer is modding their booster to add all the new mutated bits and pieces to it.

In essence the viral RNA genome enters the cell. It is then broken apart into it's subunits of smaller RNAs. These are then replicated in the cell by the ribosomes. The product of the ribosomes is then assembled into new viral genomes which usually exit the cell when it gets full and bursts - it might also use the apoptosis mechanism to release the newly made virions. These fragments are subject to mutation as the ribosome makes them = many diverse fragments, some functional and some non functional = more variants, most of which are crippled and will not work in the viral genome. The infected cell also displays these viral fragments it is busy making externally as immune system cue molecules = body creates antigens against them. This huge diversity of antigens yields a superior antigenic response to the one induced by the spike protein alone - which can miss the mutated ones. What this means is the spike protein antigens Plus all these soup to nuts antigens that you arrive at after vaccination + booster +infection is better then the fine tuned spike alone immunity.

They have (Pfizer) have sequenced the Omicron and all the prior greek letter genomes, and they have selected all the functional fragments and have created RNA strings to add to the vaccine, so when Pfizer releases it's next vaccine it will include the current new spikes Plus the RNA to make a number of these fragments. They are trying to find all the 'critical' sequences that are common to all Covid strains. Once they determine these completely they will be able to make a vaccine that stops all current as well as all new mutations. Many other companies are doing the same thing, so in a year or less a definitive vaccine will be possible.

This might mean the end of Covid, but it might not as Covid antigens fade with time. The body retain memory T cells, in small numbers, and whenever a new infection occurs it is assessed by the memory T cells and if it a known diseased, the T cell then reproduces greatly - it take 4-5 days for this response to mount, so a very efficient replicator like Omicron is capable of replicating faster than the T cell response can mount a defense = infection - usually mild and short lived as the massive T cell response will kill any infected cell once it mounts.

If you are interested and have the time, these two links go into it chapter and verses.

https://en.wikipedia.org/wiki/Immune_response

https://en.wikipedia.org/wiki/Immune_system

A recent paper also assesses the immune response to 2 vaccines + a booster + a mild infection after (or a more serious one before one or more vaccinations) as giving a very high degree of protection against all variants.