  We generalize and extend the recently proposed method to account for
contributions of system size (or volume/participant) fluctuations to the
experimentally measured moments of particle multiplicity distributions. We find
that in the general case there are additional biases which are not directly
accessible to experiment. These biases are, however, parametrically suppressed
if the multiplicity of the particles of interest is small compared to the total
charged-particle multiplicity, e.g., in the case of proton number fluctuations
at top RHIC and LHC energies. They are also small if the multiplicity
distribution of charged particles per wounded nucleon is close to the
Poissonian limit, which is the case at low energy nuclear collisions, e.g., at
GSI/SIS18. We further find that mixed events are not necessarily needed to
extract the correction for volume fluctuations, albeit it can help if event
statistics is small, which is typically the case for reconstructing the
higher-order cumulants. We provide the formulas to correct pure and mixed
cumulants of particle multiplicity distributions up to any order together with
their associated biases.
