Selecting a model topology that realistically predicts biomechanical function remains an unsolved problem. Today's dominant modeling approach is to replicate experimental input/output data by performing parameter estimation on an assumed topology. In contrast, we propose that modeling some complex biomechanical systems requires the explicit and simultaneous exploration of model topology (i.e., the type, number, and organization of physics-based functional building blocks) and parameter values. In this paper, we use the example of modeling the notoriously complex tendon networks of the fingers to present three critical advances towards the goal of implementing this extended modeling paradigm. First, we describe a novel computational environment to perform quasi-static simulations of arbitrary topologies of elastic structures undergoing large deformations. Second, we use this form of simulation to show that the assumed topology for the tendon network of a finger plays an important role in the propagation of tension to the finger joints. Third, we demonstrate the use of a novel inference algorithm that simultaneously explores the topology and parameter values for hidden synthetic tendon networks. We conclude by discussing critical issues of observability, separability, and uniqueness of topological features inferred from input/output data, and outline the challenges that need to be overcome to apply this novel modeling paradigm to extract causal models in real anatomical systems.