We have developed mechanisms for extending the functionality of the open-source Firefly astronomical visualization software with user-supplied code. Firefly is a toolkit for the construction of Web-based applications for visualizing astronomical images and tabular data, with the software distribution also including a basic general-purpose pre-built application. The Firefly tools are the base for NASA's IRSA archive as well as other web applications developed at IPAC. Recent releases include new public APIs allowing the extension of Firefly functionality in various ways. New Javascript APIs allow customization of the interface presented in the browser, including the ability to define buttons for custom actions that can be performed on points, lines, and regions in images. New Python APIs allow the invocation of operations in a Firefly-based application, allowing it to serve as a display engine for FITS images and other astronomical data. In addition, the Firefly web server side has been enhanced with the ability to invoke user-supplied processes that can produce either image or tabular results based on operations on data from the application or external sources. For instance, the user can define an operation to perform source detection on a graphically selected region in an image and return the results for display as a table and/or x-y plot. User processes can be defined in any language supported on the server host; our current efforts have focused on Python. This mechanism has been used to support the integration of Firefly with the LSST project's software stack, with reusable "tasks" from the LSST stack configurable as extensions to Firefly.