Microseismic data and post-fracturing production have confirmed the positive role of fracture complexity on production enhancement in fractured wells. While operators are looking for different fluids and pumping schedules to enhance fracture complexity, the mechanisms ruling the process is not fully understood. This paper provides a comprehensive workflow to model the fracture pattern development by accounting for interactions with numerous natural fractures. We present a robust finite element model with adaptive insertion of three-dimensional cohesive elements for fracture propagation through the intact rock as well as the network of intersecting natural fractures. Cohesive elements are coupled with general Darcy's flow to incorporate fluid flow as well as elastic and plastic deformations of rock during initiation, propagation and closure of hydraulic fractures. Hydraulic fracturing treatment has been simulated for different natural fracture patterns. Fluid injection pressure fluctuations are observed while reopening natural fractures. The impact of operation schedules on network complexity such as hesitation time is investigated. The complexity of fracture network is characterized by the ratio of total fracture length to its effective radius from the wellbore. Our analysis has shown that in addition to the differential stress and the fracture intersection angle which are already determined by the nature, pumping injection rate and hesitation time can play a significant role in fracture branching and its diversion to different natural fracture sets. Higher injection rate is found to have a positive effect to overcome the resistance of natural fractures in different directions, and hesitation in the middle of pumping can force the fracture to divert into other directions, both of which help develop a more complex fracture pattern.