  A superconductor with 4-fermion attraction, considered by Ma\'{c}kowiak and
Tarasewicz is modified by adding to the Hamiltonian a long-range magnetic
interaction $V$ between conduction fermions and localized distinguishable spin
1/2 magnetic impurities. $V$ has the form of a reduced s-d interaction. An
upper and lower bound to the system's free energy density $f(H,\beta)$ is
derived and the two bounds are shown to coalesce in the thermodynamic limit.
The resulting mean-field equations for the gap $\Delta$ and a parameter $y$,
characterizing the impurity subsystem are solved and the solution minimizing
$f$ is found for various values of magnetic coupling constant $g$ and impurity
concentration. The phase diagrams of the system are depicted with five distinct
phases: the normal phase, unperturbed superconducting phase, perturbed
superconducting phase with nonzero gap in the excitation spectrum, perturbed
gapless superconducting phase and impurity phase with completely suppressed
superconductivity.
