There has been an explosion of ideas in soft robotics over the past decade, resulting in unprecedented opportunities for end effector design. Soft robot hands offer benefits of low-cost, compliance, and customized design, with the promise of dexterity and robustness. The space of opportunities is vast and exciting. However, new tools are needed to understand the capabilities of such manipulators and to facilitate manipulation planning with soft manipulators that exhibit free-form deformations. To address this challenge, we introduce a sampling based approach to discover and model continuous families of manipulations for soft robot hands. We give an overview of the soft foam robots in production in our lab and describe novel algorithms developed to characterize manipulation families for such robots. Our approach consists of sampling a space of manipulation actions, constructing Gaussian Mixture Model representations covering successful regions, and refining the results to create continuous successful regions representing the manipulation family. The space of manipulation actions is very high dimensional; we consider models with and without dimensionality reduction and provide a rigorous approach to compare models across different dimensions by comparing coverage of an unbiased test dataset in the full dimensional parameter space. Results show that some dimensionality reduction is typically useful in populating the models, but without our technique, the amount of dimensionality reduction to use is difficult to predict ahead of time and can depend on the hand and task. The models we produce can be used to plan and carry out successful, robust manipulation actions and to compare competing robot hand designs.