Biradial symmetry occurs in ctenophores: the body plan consists of two halves which independently display radial symmetry. Spherical symmetry occurs in Volvox algae: any cut through the center of the body results in two identical halves.
Hypothetically, an organism could display spherical symmetry. For example, an organism resembling the mythical amphisbaena with a head analogue at either end of its body.
How plausible is a spherically symmetrical body plan in animals, or at least in basal animals or ancestors of derived animals that discarded this symmetry?
EDIT: Spherical doesn't have to be literal. The organisms might be worm like with a gut that opens at both ends, but the gut orifices are two way or the anus is located ventrally. I expect that as the spherical symmetry organisms grow larger and enter more niches they would undergo cephalisation.
I would think there would be vestiges of their ancestral symmetry. Similar arrangements of body parts in front and back? Vertebrates have two eyes and two gonads by chance, but maybe in this organism the eyes and gonads develop from similar embryonic structures? If the basal gut was a two-way tube, then maybe the derived organisms have a anus in the ventral region rather than the posterior?