This paper proposes a general Mixed-Integer Nonlinear Programming (MINLP) formulation for the optimal design of multiphase pipeline networks gathering oil and gas production from wellpads. In contrast to previous approaches, the model explicitly incorporates nonlinear correlations to predict multiphase pressure losses accurately, enabling a more rigorous optimization of the network design and pipeline sizes. Gathering flows according to production start times, wellhead pressures, and gas-to-oil ratios proves essential to secure production, while simultaneously maximizing transportation capacity and minimizing surface facility costs. The model is able to effectively manage flow pressures at junction nodes, compositions after merging, and flexible network topologies. An efficient successive-relaxation approach based on piecewise-constant underestimations of pressure drops is also proposed to obtain solutions within reasonable computation times. Results show that relaxing the limiting assumptions imposed by previous approaches leads to improvements of up to 20% in the net present value (NPV) of illustrative cases comprising ten wellpads. However, the global optimization of real-size problems with more complex topologies remains a significant challenge.