An important sub-topic in survivable topology design is the augmentation of existing topologies to enable surviving node or link failures. The general topology augmentation problem addresses the general question: what additional resources are required to build upon an existing network to enhance its survivability? A typical such problem involves finding the fewest links to add to a topology to make the topology 2-edge-connected. This paper considers a variation of that problem: given a topology, a set of potential links each with a cost, and a limited budget, find links that can be added to enhance the topology's biconnectivity. This variation is useful for the case where expansion of a topology is constrained by a limited budget. The problem is shown to be NP-complete. Three simple heuristics are presented and evaluated through experimentation. The main result is that simple greedy heuristics that reduce cost are not effective because the problem structure combines both costs and paths in unusual ways. Instead, a suite of heuristics appears to perform effectively.