  Staggered fermion shift symmetries correspond to translations within the unit
cell of a hypercubic lattice. They satisfy an algebra and in four Euclidean
dimensions can be related to a discrete subgroup of $SU(4)$ which plays a
crucial role in showing that staggered fermions lead to a theory of four
degenerate Dirac fermions in the continuum limit. They are associated with the
appearance of certain $Z_2$ valued global parameters. We propose a strategy to
try to partially gauge these translation symmetries by allowing these
parameters to vary locally in the lattice. To maintain invariance of the action
requires the addition of $Z_2$ valued higher form gauge fields. We show how
there is a geometrical obstruction to this procedure in the case of full
staggered fermions which is consistent with the existence of a 't Hooft anomaly
in the continuum $SU(4)$ flavor symmetry. However no such obstruction is
encountered for reduced staggered fermions for which the continuum
non-anomalous flavor symmetry is $SO(4)$.
