A concept of modular textile antenna design with commercial snap-on buttons has been proposed recently for wearable applications. The concept was shown to provide passive system reconfigurabilities in regard to resonance frequency and polarization without modifications to the feeding structure. As an extension of this work, a foldable patch module is presented in this paper for the antenna concept, demonstrating further passive discrete resonance frequency modularity at 8, 9 and 10 GHz. Through a simple folding of the textile radiating element at predetermined lengths denoted by position markers, particular resonance frequencies can be manually interchanged. Prototype-based experimental characterization shows a good agreement with simulations, which indicates that the foldable module performs as expected. This design emphasizes that the reported modular antenna design promotes a practical, low-manufacture-cost, low-maintenance-cost, passive and versatile solution to reconfigure system characteristics for multi-functional wearable systems.