The interaction of supernova fragments with the internal structure of large multisupernova remnants (MSRs) is studied with analytical approximations and two-dimensional hydrodynamical simulations. The fragments are thermalized by reverse shocks generated in the interaction with the MSR interior, which is assumed to be hot (T is similar to 10(7) K) and rarefied (with a gas density n is similar to 10(-2) to 10(-3) cm-3). The density and velocity stratifications of the supernova ejecta, which define the fragment properties, are taken from recent explosion models for Type II supernova. The evolution can be divided in two stages: before and after reaching a reference distance, R(E) (where the fragment has been eroded by 5%), from the explosion site. At early times, when located interior to R(E), the fragment expands almost freely because the reverse shock is not able to penetrate to a significant depth (the reverse shock speed remains low because the fragment density is substantially higher than the MSR interior density). As the density of the expanding fragment drops, the reverse shock accelerates, and, when the distance R(E) is reached, it begins to effectively erode the fragment. The erosion process is followed with both analytical approximations and numerical simulations, and we find a very good agreement between the two methods. At some selected evolutionary times, the X-ray emission from the shocked fragment is also calculated. When sequential SN explosions are considered, the key issue in the evolution of a multisupernova remnant is whether or not the fragments can survive until they collide with the MSR shell. This '' bombardment '' phase can last for about a few million years (or, at typical SN explosion rates on OB associations, up to the first approximated five to 10 explosions). This direct bombardment of the MSR shell has a series of important consequences: it excites, punctures, and deforms the expanding shell.