We introduce PuppetAI, a modular soft robot interaction platform. This platform offers a scalable cable-driven actuation system and a customizable, puppet-inspired robot gesture framework, supporting a multitude of interaction gesture robot design formats. The platform comprises a four-layer decoupled software architecture that includes perceptual processing, affective modeling, motion scheduling, and low-level actuation. We also implemented an affective expression loop that connects human input to the robot platform by producing real-time emotional gestural responses to human vocal input. For our own designs, we have worked with nuanced gestures enacted by "soft robots" with enhanced dexterity and "pleasant-to-touch" plush exteriors. By reducing operational complexity and production costs while enhancing customizability, our work creates an adaptable and accessible foundation for future tactile-based expressive robot research. Our goal is to provide a platform that allows researchers to independently construct or refine highly specific gestures and movements performed by social robots.