  We use Gaia EDR3 data to identify stars associated with six classical dwarf
spheroidals (Draco, Ursa Minor, Sextans, Sculptor, Fornax, Carina) at their
outermost radii, beyond their nominal King stellar limiting radius. For all of
the dSphs examined, we find radial velocity matches with stars residing beyond
the King limiting radius and with $> 50\%$ astrometric probability (four in
Draco, two in Ursa Minor, eight in Sextans, two in Sculptor, twelve in Fornax,
and five in Carina), indicating that these stars are associated with their
respective dwarf spheroidals (dSphs) at high probability. We compare the
positions of our candidate "extra-tidal" stars with the orbital tracks of the
galaxies, and identify stars, both with and without radial velocity matches,
that are consistent with lying along the orbital track of the satellites.
However, given the small number of candidate stars, we cannot make any
conclusive statements about the significance of these spatially correlated
stars. Cross matching with publicly available catalogs of RR Lyrae, we find one
RR Lyrae candidate with $> 50\%$ astrometric probability outside the limiting
radius in each of Sculptor and Fornax, two such candidates in Draco, nine in
Ursa Minor, seven in Sextans, and zero in Carina. Follow-up spectra on all of
our candidates, including possible metallicity information, will help confirm
association with their respective dSphs, and could represent evidence for
extended stellar halos or tidal debris around these classical dSphs.
