  A considerable number of semi-empirical and first-principles models have been
created to describe the dynamic response of a collisionally damped
charged-particle system. However, known challenges persist for established
dynamic structure factors (DSF), dielectric functions, and conductivities. For
instance, the semi-empirical Drude-Smith conductivity [N.M. Smith, Phys. Rev. B
64, 155106 (2001)] lacks interpretability, and the first-principles Mermin
dielectric function [N.D. Mermin, Phys. Rev. B, 1, 2362 (1970)] does not
satisfy the frequency sum rule [G.S. Atwal and N.W. Ashcroft, Phys. Rev. B 65,
115109 (2002)]. In this work, starting from the multicomponent
Bhatnagar-Gross-Krook (BGK) kinetic equation, we produce a multi-species
susceptibility that conserves number and momentum, which we refer to as the
``completed Mermin'' susceptibility, and we explore its properties and uses. We
show that the completed Mermin susceptibility satisfies the frequency sum
(f-sum) rule. We compute the associated DSF and find that momentum conservation
qualitatively impacts the DSF's shape for a carbon-contaminated deuterium and
tritium plasma under NIF hot-spot conditions. In the appendices, we provide
numerical implementations of the completed Mermin susceptibility, for the
reader's convenience. Further, we produce a new non-Drude conductivity model,
by taking the single-species limit and introducing free parameters in the terms
that enforce number and momentum conservation. To illustrate how number and
momentum conservation impact the dynamical conductivity shape, we apply our
conductivity model to dynamical gold conductivity measurements [Z. Chen, et
al., Nature communications, 12.1, 1638, (2021)]. Finally, comparing our model
to the Drude-Smith conductivity model, we conclude that Smith's
phenomenological parameter violates local number conservation.
