Aims. We present the implementation of a coupling between EUropean Heliospheric FORcasting Information Asset (EUHFORIA) and improved Particle Acceleration and Transport in the Heliosphere (iPATH) models. In this work, we simulate the widespread solar energetic particle (SEP) event of 2020 November 29 and compare the simulated time-intensity profiles with measurements at Parker Solar Probe (PSP), the Solar Terrestrial Relations Observatory (STEREO)-A, SOlar and Heliospheric Observatory (SOHO), and Solar Orbiter (SolO). We focus on the influence of the history of shock acceleration on the varying SEP time-intensity profiles and investigate the underlying causes in the origin of this widespread SEP event.Methods. We simulated a magnetized coronal mass ejection (CME) propagating in the data-driven solar wind with the EUHFORIA code. The CME was initiated by using the linear force-free spheromak module of EUHFORIA. The shock parameters and a 3D shell structure were computed from EUHFORIA as inputs for the iPATH model. Within the iPATH model, the steady-state solution of particle distribution assuming diffuse shock acceleration is obtained at the shock front. The subsequent SEP transport is described by the focused transport equation using the backward stochastic differential equation method with perpendicular diffusion included. Results. We examined the temporal evolution of shock parameters and particle fluxes during this event and we find that adopting a realistic solar wind background can significantly impact the expansion of the shock and, consequently, the shock parameters. Timeintensity profiles with an energetic storm particle event at PSP are well reproduced from the simulations. In addition, the simulated and observed time-intensity profiles of protons show a similar two-phase enhancement at STA. These results illustrate that modeling a shock using a realistic solar wind is crucial in determining the characteristics of SEP events. The decay phase of the modeled time-intensity profiles at Earth is in good agreement with the observations, indicating the importance of perpendicular diffusion in widespread SEP events. Taking into account the possible large curved magnetic field line connecting to SolO, the modeled timeintensity profiles show a good agreement with the observation. We suggest that the broadly distorted magnetic field lines, which are due to a stream interaction region, may be a key factor in helping to improve our understanding of the observed SEPs at SolO for this event.