  We consider a new type of ${\cal N}=4$, $d=1$ semi-dynamical multiplet based
on the non-linear version of the mirror multiplet ${\bf (3, 4, 1)}$, with the
triplet of bosonic physical fields parametrizing a three-dimensional sphere
$S^3$ of the radius $R$. The limit $R\to\infty$ amounts to the contraction
$S^3\to\mathbb{R}^3$ and leads to the linear mirror multiplet ${\bf (3, 4,
1)}$. Spin degrees of freedom described by a Wess-Zumino action specify a
two-dimensional surface embedded in the sphere $S^3$. A pair of the examples
considered correspond to the round and squashed ``fuzzy'' 2-spheres. We couple
the squashed 2-sphere model to the dynamical mirror multiplet ${\bf (2, 4,
2)}$. A notable feature of this coupling is the dependence of the squashing
parameter on the bosonic fields $z, \bar z$ of the chiral multiplet.
