  Extensions of the minimal supersymmetric standard model (MSSM) gauge group
abound in the literature. Several of these include an additional $U(1)_X$ gauge
group. Chiral fermions' charge assignments under $U(1)_X$ are constrained to
cancel local anomalies in the extension and they determine the structure and
phenomenology of it. We provide all anomaly-free charge assignments up to a
maximum absolute charge of $Q_\text{max}=10$, assuming that the chiral
superfield content of the model is that of the MSSM plus up to three Standard
Model (SM) singlet superfields. The fermionic components of these SM singlets
may play the r\^{o}le of right-handed neutrinos, whereas one of the scalar
components may play the r\^{o}le of the flavon, spontaneously breaking
$U(1)_X$. Easily scanned lists of the charge assignments are made publicly
available on Zenodo. For the case where no restriction is placed upon
$Q_\text{max}$, we also provide an analytic parameterisation of the general
solution using simple techniques from algebraic geometry.
