We study numerically noise-like pulsing in a long passively mode-locked figure-eight fibre laser with a polarization-imbalanced nonlinear optical loop mirror (NOLM) and a strong dispersion map. Contrary to the common scenario where a single noise-like pulse develops, it is found that multiple small bunches tend to form in the cavity, sharing roughly the same characteristics, which are determined by the dispersion parameters. The wave packets are subject to ample periodic variations of their duration and peak intensity as they pass through sections of opposite dispersion signs, displaying a breathing dynamics analogous to the one undergone by solitons in stretched-pulse fibre lasers. Multiple noise-like pulsing operation can be understood by considering the strong compression and corresponding intensity increase of small bunches as they travel through the NOLM, which yields higher transmission through the NOLM and thus smaller cavity losses for these small units than for larger wave packets. The present results could serve as a basis for a deeper study of the dynamics taking place in partially mode-locked fibre sources, which is particularly complex when multiple bunches of radiation coexist and interact in the cavity.