  This paper is devoted to the systematic study of additional (non-
isospectral) symmetries of constrained (reduced) supersymmetric integrable
hierarchies of KP type- the so called SKP_(R;M_B,M_F) models. The latter are
supersymmetric extensions of ordinary constrained KP hierarchies which contain
as special cases basic integrable systems such as (m)KdV, AKNS, Fordy-Kulish,
Yajima- Oikawa etc.. As a first main result it is shown that any
SKP_(R;M_B,M_F) hierarchy possesses two different mutually (anti-)commuting
types of superloop superalgebra additional symmetries corresponding to the
positive-grade and negative-grade parts of certain superloop superalgebras. The
second main result is the systematic construction of the full algebra of
additional Virasoro symmetries of SKP_(R;M_B,M_F) hierarchies, which requires
non- trivial modifications of the Virasoro flows known from the general case of
unconstrained Manin-Radul super-KP hierarchies (the latter flows do not define
symmetries for constrained SKP_(R;M_B,M_F) hierarchies). As a third main result
we provide systematic construction of the supersymmetric analogues of
multi-component (matrix) KP hierarchies and show that the latter contain among
others the supersymmetric version of Davey-Stewartson system. Finally, we
present an explicit derivation of the general Darboux- B\"acklund solutions for
the SKP_(R;M_B,M_F) super-tau functions (supersymmetric ``soliton''-like
solutions) which preserve the additional (non-isospectral) symmetries.
