  We couple two copies of the supersymmetric mKdV hierarchy by means of the
algebraic dressing technique. This allows to deduce the whole set of $(N,N)$
supersymmetry transformations of the relativistic sector of the extended mKdV
hierarchy and to interpret them as fermionic symmetry flows. The construction
is based on an extended Riemann-Hilbert problem for affine Kac-Moody
superalgebras with a half-integer gradation. A generalized set of
relativistic-like fermionic local current identities is introduced and it is
shown that the simplest one, corresponding to the lowest isospectral times
$t_{\pm 1}$ provides the supercharges generating rigid supersymmetry
transformations in 2D superspace. The number of supercharges is equal to the
dimension of the fermionic kernel of a given semisimple element $E \in
\widehat{\mathfrak{g}}$ which defines both, the physical degrees of freedom and
the symmetries of the model. The general construction is applied to the
$N=(1,1)$ and $N=(2,2)$ sinh-Gordon models which are worked out in detail.
