Two more solutions for the parafermionic chiral algebra Z_{3} with the dimension of the principal parafermionic fields, psi(z), psi^{+}(z), Delta_{psi}=8/3

In this paper, which is the second one in a series of two papers, we shall present two more solutions, non-minimal ones, for the Z_{3} parafermionic chiral algebra with Delta_{psi}=Delta_{psi^{+}}=8/3, psi(z), psi^{+}(z) being the principal parafermionic fields.