An intense solar energetic particle (SEP) event was observed on 2021 October 9 by multiple spacecraft distributed near the ecliptic plane at heliocentric radial distances R ≲ 1 au and within a narrow range of heliolongitudes. A stream interaction region (SIR), sequentially observed by Parker Solar Probe (PSP) at R = 0.76 au and 48° east from Earth (ϕ = E48°), STEREO-A (at R = 0.96 au, ϕ = E39°), Solar Orbiter (SolO; at R = 0.68 au, ϕ = E15°), BepiColombo (at R = 0.33 au, ϕ = W02°), and near-Earth spacecraft, regulated the observed intensity-time profiles and the anisotropic character of the SEP event. PSP, STEREO-A, and SolO detected strong anisotropies at the onset of the SEP event, which resulted from the fact that PSP and STEREO-A were in the declining-speed region of the solar wind stream responsible for the SIR and from the passage of a steady magnetic field structure by SolO during the onset of the event. By contrast, the intensity-time profiles observed near Earth displayed a delayed onset at proton energies ≳13 MeV and an accumulation of ≲5 MeV protons between the SIR and the shock driven by the parent coronal mass ejection (CME). Even though BepiColombo, STEREO-A, and SolO were nominally connected to the same region of the Sun, the intensity-time profiles at BepiColombo resemble those observed near Earth, with the bulk of low-energy ions also confined between the SIR and the CME-driven shock. This event exemplifies the impact that intervening large-scale interplanetary structures, such as corotating SIRs, have in shaping the properties of SEP events.