Coronal mass ejections (CMEs) drive powerful shocks and thereby accelerate solar energetic particles (SEPs) as they propagate from the corona into interplanetary space. Here we present the processes of three-stage particle acceleration by a CME-driven shock detected by the in situ spacecraft—Parker Solar Probe (PSP) on 2022 August 27. The onset of SEPs is produced by a fast CME with a speed of 1284 km s−1 when it propagates to ∼2.85 R ⊙. The second stage of particle acceleration occurs when the fast CME catches up and interacts with a preceding slow one in interplanetary space at ∼40 R ⊙ (∼0.19 au). The CME interaction is accompanied by an intense interplanetary type II radio enhancement. Such direct measurement of particle acceleration during interplanetary CME interaction/radio enhancement is rarely recorded in previous studies. The third stage of energetic storm particles is associated with the CME-driven shock passage of the PSP at ∼0.38 au. Obviously, harder particle spectra are found in the latter two stages than the first one, which can arise from a stronger shock produced by the CME interaction and the enriched seed particles inside the preceding CME.