Extreme-amplitude events and rare instabilities are observed for more than a decade in various optical systems. Specifically in dissipative systems, such as Raman fiber lasers, laser diodes or mode-locked lasers, to name a few, long-tailed statistics and highly-localized temporal structures have been observed [1,2]. Recent studies showed that stimulated Brillouin scattering (SBS) can also trigger the generation of extreme events in various configurations, from self-pulsing fiber lasers [3,4] to Q-switched random fiber lasers [5]. It is indeed known that the stochastic nature of SBS can promote the emergence of randomly distributed giant pulses which can induce irreversible damages in fiber laser systems. In order to understand and open the possibility to harness such extreme events, numerical models have then to be developed and refined. In the context of self-pulsed fiber lasers, a few studies taking into account only one or two fundamental Stokes orders have already been reported [6]. Such models describe well the large pulse-to-pulse intensity fluctuations observed in Erbium-doped fiber lasers Q-switched through SBS but they however did not predict any extreme event [6]. We propose here an extension of the model proposed in Ref. [3] by generalizing it to higher Stokes orders to study their impact on extreme dynamics in a self-pulsing laser. Our model is based on the coupled amplitudes equations describing the spatiotemporal dynamics of both the laser and Brillouin waves with their corresponding acoustic fields, as well as the temporal variations of the gain for each wave. We also consider a matter equation to account for the saturable absorption effect which can occur in the un-pumped segment of the active fiber. We show that increasing the number of SBS orders interacting with the gain medium reveals new dynamics enabling the generation of extreme events which are not predicted by the single SBS order model. Pulses with amplitudes 27 times the so-called signific...