Our task in this paper consists in reconstructing the four-particle scattering theory so as to be useful in practical applications. From this point of view, the integral equation for the four-particle scattering matrix, given in a previous paper is extended to a more useful one, in which the kernel is separated into two parts; one refers to the scattering matrix between an arbitrary three-particle subsystem and a free particle, and the other to the scattering matrix between two two-particle subsystems. By using these equations, as will be shown, the treatment of practical problems becomes quite convenient. We discuss, as a case of special interest, composite-composite particle scattering in the four-particle system, by approximating the two two-particle subsystems by bound-state and/or resonance poles.