Cardiolipin (CL) is a negatively charged four acyl chain lipid, associated with energy production in bacterial and mitochondrial membranes. Due to the shape of CL, negative curvatures of aggregates are favorable if the charges in the head group can be reduced. The phase polymorphism of CL, and of associated derivatives with 2, 3, 4, or 5 chains, has been determined previously and offers a model system in which micellar, lamellar, and inverse hexagonal phases can be observed. We present an extension to a previously established coarse-grained molecular dynamics model with the aim of reproducing the different CL phases with two adjustable parameters: the number of acyl chains and the effective head group charge. With molecular dynamics simulations of large lipid systems, we observed transitions between different phases on the nanosecond to microsecond time scale. Charge screening by high salt or low pH was successfully modeled by a reduction of phosphate charge, which led to the adoption of aggregates with more negative curvature. Although specific ion binding at the interface and other atomistic details are sacrificed in the coarse-grained model, we found that it captures general phase features over a large range of aggregate geometries.