Modifications to open-source software (OSS) are often provided in the form of "patch stacks" - sets of changes (patches) that modify a given body of source code. Maintaining patch stacks over extended periods of time is problematic when the underlying base project changes frequently. This necessitates a continuous and engineering-intensive adaptation of the stack. Nonetheless, long-term maintenance is an important problem for changes that are not integrated into projects, for instance when they are controversial or only of value to a limited group of users. We present and implement a methodology to systematically examine the temporal evolution of patch stacks, track non-functional properties like integrability and maintainability, and estimate the eventual economic and engineering effort required to successfully develop and maintain patch stacks. Our results provide a basis for quantitative research on patch stacks, including statistical analyses and other methods that lead to actionable advice on the construction and long-term maintenance of custom extensions to OSS.