To my knowledge, the first generation prevented infection from 2 strains. The second generation added 2 more. Eventually, Gardasil-9 came out, protecting agains

To my knowledge, the first generation prevented infection from 2 strains. The second generation added 2 more. Eventually, Gardasil-9 came out, protecting against 9 strains. But these are all precise genetic vaccines that should not affect non-included strains; they don't generally activate the immune system at large (hence their safety). Perhaps something changed since I stopped reading papers about it?