Content Distribution Networks (CDNs) play a crucial role in efficiently delivering online content to end-users. In this paper, we initiate the study of CDN domain planning with flexible assignments of domains to Points of Presence (PoPs) within a CDN, with the objective of minimizing the cost of transmissions while providing sufficient resources to serve the communication demands. The problem is subject to practical constraints of network deployment such as a percentile-based billing model, PoP's bandwidth and committed rate limits, geographic locality and quota constraints and minimum per domain cache-hit-ratios. We formulate the problem as an offline optimization task with a nonlinear objective function and linear constraints, which becomes computationally intensive for medium-sized instances. The 95th percentile billing model, commonly used by service providers, contributes significantly to this non-linearity. To address this, we propose Baiji, a multi-algorithm approach lever- aging insights from our formulation. Our empirical evaluation of Baiji on two synthetic and one real-world workloads demonstrates its effectiveness in approaching the upper bound on system performance. Baiji provides high-quality solutions for CDN monthly planning, with tunable execution times (from tens of seconds up to four hours), making Baiji suitable for practical deployment in CDNs.