  In this work we classify all smooth surfaces with geometric genus equal to
three and an action of a group G isomorphic to (Z/2)^k such that the quotient
is a plane. We find 11 families. We compute the canonical map of all of them,
finding in particular a family of surfaces with canonical map of degree 16 that
we could not find in the literature. We discuss the quotients by all subgroups
of G finding several K3 surfaces with symplectic involutions. In particular we
show that six families are families of triple K3 burgers in the sense of
Laterveer.
