  We investigate integrable fermionic models within the scheme of the graded
Quantum Inverse Scattering Method, and prove that any symmetry imposed on the
solution of the Yang-Baxter Equation reflects on the constants of motion of the
model; generalizations with respect to known results are discussed. This
theorem is shown to be very effective when combined with the Polynomial
$\Rc$-matrix Technique (PRT): we apply both of them to the study of the
extended Hubbard models, for which we find all the subcases enjoying several
kinds of (super)symmetries. In particular, we derive a geometrical construction
expressing any $gl(2,1)$-invariant model as a linear combination of EKS and
U-supersymmetric models. Furtherly, we use the PRT to obtain 32 integrable
$so(4)$-invariant models. By joint use of the Sutherland's Species technique
and $\eta$-pairs construction we propose a general method to derive their
physical features, and we provide some explicit results.
