  Semichiral $(2,2)$ sigma models with $4d$ target space are discussed. A novel
description in $(1,1)$ superspace allows an analysis of possible extended
supersymmetries. It is argued that a manifest semichiral realization of an
extra supersymmetry is only possible for hyperk\"ahler target geometry. A
semichiral formulation of the $SU(2)\otimes U(1)$ WZW model is seemingly a
counterexample to this. After deriving the extra supersymmetries of this model
in $(1,1)$ superspace it is shown that they cannot be lifted to transformations
of semichirals in $(2,2)$ superspace.
