  While protoplanetary disks are often treated as isolated systems in planet
formation models, observations increasingly suggest that vigorous interactions
between Class II disks and their environments are not rare. DO Tau is a T Tauri
star that has previously been hypothesized to have undergone a close encounter
with the HV Tau system. As part of the DESTINYS ESO Large Programme, we present
new VLT/SPHERE polarimetric observations of DO Tau and combine them with
archival HST scattered light images and ALMA observations of CO isotopologues
and CS to map a network of complex structures. The SPHERE and ALMA observations
show that the circumstellar disk is connected to arms extending out to several
hundred au. HST and ALMA also reveal stream-like structures northeast of DO
Tau, some of which are at least several thousand au long. These streams appear
not to be gravitationally bound to DO Tau, and comparisons with previous
Herschel far-IR observations suggest that the streams are part of a bridge-like
structure connecting DO Tau and HV Tau. We also detect a fainter redshifted
counterpart to a previously known blueshifted CO outflow. While some of DO
Tau's complex structures could be attributed to a recent disk-disk encounter,
they might be explained alternatively by interactions with remnant material
from the star formation process. These panchromatic observations of DO Tau
highlight the need to contextualize the evolution of Class II disks by
examining processes occurring over a wide range of size scales.
