This paper describes recent upgrades of TOPICA (Torino Politecnico Ion Cyclotron Antennas) formulation and implementation. TOPICA is a code capable of handling both the actual geometry of ion cyclotron (IC) antennas and an accurate plasma description; it can predict the performances of IC launchers with an unprecedented accuracy and numerical efficiency, validated against data measured in plasma operation conditions. In the reported upgrade, a new multi-cavity approach is introduced, producing significant savings in terms of CPU and memory requirements and allowing the analysis of large antennas even with limited computational resources. In fact, by formally separating the structure's cavities with a number of mathematical surfaces called ‘apertures’, the method of moments interaction matrix is block-wise sparse and, as a consequence, can be manipulated with a far higher numerical efficiency; this also allows an out-of-core solution.