Increasing grid integration of intermittent renewable energy sources (RESs) and plug-in electric vehicles (PEVs) with uncertain behaviours have necessitated enhancing the flexibility requirements of distribution networks. Thus, in the state-of-the-art distribution network expansion planning (DNEP) models, both flexibility requirements and high penetration of RESs and PEVs should be taken into consideration. In this respect, a novel collaborative planning model for power distribution network (PDN) and plug-in Electric Vehicle Parking Lots (EVPLs) is proposed in this paper, which leverages sizing, siting, and operation of EVPLs to enhance the distribution network flexibility. Also, to model the uncertain traffic flow of PEVs, a new model is proposed and is utilized to obtain a preliminary dispatch of PEV charging and, in turn, an estimated EVPL demand. Afterwards, this estimated demand is fed into the collaborative planning model to obtain the optimal expansion planning solution for PDN, and the size and location of EVPLs. Nonetheless, to provide the network operator with more flexibility sources, it is assumed that the operator can reschedule the charging pattern of some PEVs by compensating the EVPL owners for the difference in retail electricity prices of various hours. Finally, to illustrate the effectiveness of the proposed model, it is implemented on a test network, and the obtained results are discussed.