  We present follow-up photometry and spectroscopy of ZTF J0328$-$1219
strengthening its status as a white dwarf exhibiting transiting planetary
debris. Using TESS and Zwicky Transient Facility photometry, along with
follow-up high speed photometry from various observatories, we find evidence
for two significant periods of variability at 9.937 and 11.2 hr. We interpret
these as most likely the orbital periods of different debris clumps. Changes in
the detailed dip structures within the light curves are observed on nightly,
weekly, and monthly timescales, reminiscent of the dynamic behavior observed in
the first white dwarf discovered to harbor a disintegrating asteroid, WD
1145+017. We fit previously published spectroscopy along with broadband
photometry to obtain new atmospheric parameters for the white dwarf, with
$M_{\star} = 0.731 \pm 0.023\,M_{\odot}$, $T_{\mathrm{eff}} = 7630 \pm 140\,$K,
and $\mathrm{[Ca/He]}=-9.55\pm0.12$. With new high-resolution spectroscopy, we
detect prominent and narrow Na D absorption features likely of circumstellar
origin, with velocities $21.4\pm1.0$ km s$^{-1}$ blue-shifted relative to
atmospheric lines. We attribute the periodically modulated photometric signal
to dusty effluents from small orbiting bodies such as asteroids or comets, but
are unable to identify the most likely material that is being sublimated, or
otherwise ejected, as the environmental temperatures range from roughly 400K to
600K.
