We introduce and study two new classes of unital quantum channels. The first class describes a 2-parameter family of channels given by completely positive (CP) maps M₃(C) ↦ M₃(C) which are both unital and trace-preserving. Almost every member of this family is factorizable and extreme in the set of CP maps which are both unital and trace-preserving, but is not extreme in either the set of unital CP maps or the set of trace-preserving CP maps. We also study a large class of maps which generalize the Werner-Holevo channel for d= 3 in the sense that they are defined in terms of partial isometries of rank d- 1. Moreover, we extend this to maps whose Kraus operators have the form t|ej⟩⟨ej|⊕V with V∈ M_d-1(C) unitary and t∈ (- 1 , 1). We show that almost every map in this class is extreme in both the set of unital CP maps and the set of trace-preserving CP maps. We analyze in detail a particularly interesting family which is extreme unless t=-1d-1. For d= 3 , this includes a pair of channels which have a dual factorization in the sense that they can be obtained by taking the partial trace over different subspaces after using the same unitary conjugation in M₃(C) ⊗ M₃(C).