  The deformation approach of arXiv:2104.07816 for computing zeta functions of
one-parameter Calabi-Yau threefolds is generalised to cover also multiparameter
manifolds. Consideration of the multiparameter case requires the development of
an improved formalism. This allows us, among other things, to make progress on
some issues left open in previous work, such as the treatment of apparent and
conifold singularities and changes of coordinates. We also discuss the
efficient numerical computation of the zeta functions. As examples, we compute
the zeta functions of the two-parameter mirror octic, a non-symmetric split of
the quintic threefold also with two parameters, and the $S_5$ symmetric
five-parameter Hulek-Verrill manifolds. These examples allow us to exhibit the
several new types of geometries for which our methods make practical
computations possible. They also act as consistency checks, as our results
reproduce and extend those of arXiv:hep-th/0409202 and arXiv:math/0304169. To
make the methods developed here more approachable, a Mathematica package
"CY3Zeta" for computing the zeta functions of Calabi-Yau threefolds, which is
attached to this paper, is presented.
