  We present several infinite families of potential modular data motivated by
examples of Drinfeld centers of quadratic categories. In each case, the input
is a pair of involutive metric groups with Gauss sums differing by a sign,
along with some conditions on the fixed points of the involutions and the
relative sizes of the groups. From this input we construct $S$ and $T$ matrices
which satisfy the modular relations and whose Verlinde coefficients are
non-negative integers. We also check certain restrictions coming from
Frobenius-Schur indicators.
  These families generalize Evans and Gannon's conjectures for the modular data
associated to generalized Haagerup and near-group categories for odd groups,
and include the modular data of the Drinfeld centers of almost all known
quadratic categories. In addition to the subfamilies which are conjecturally
realized by centers of quadratic categories, these families include many
examples of potential modular data which do not correspond to known types of
modular tensor categories.
