  Generalizing work of I. Baykur, K. Hayano, and N. Monden (arXiv:1903.02906),
we construct infinite families of symplectic 4-dimensional manifolds, obtained
as total spaces of Lefschetz pencils constructed by explicit monodromy
factorizations. Then, generalizing work of the author (arXiv:2108.04868), we
show that each of these manifolds is diffeomorphic to a complex surface that is
a fiber sum formed from two standard examples of hyperelliptic Lefschetz
fibrations. Consequently, we see that these hyperelliptic Lefschetz fibrations,
as well as all fiber sums of them, admit an infinite family of explicitly
described Lefschetz pencils, which we observe are different from families
formed by the degree doubling procedure.
