In this paper we propose a technique to adapt a convolutional neural network (CNN) based object counter to additional visual domains and object types while still preserving the original counting function. Domain-specific normalisation and scaling operators are trained to allow the model to adjust to the statistical distributions of the various visual domains. The developed adaptation technique is used to produce a singular patch-based counting regressor capable of counting various object types including people, vehicles, cell nuclei and wildlife. As part of this study a challenging new cell counting dataset in the context of tissue culture and patient diagnosis is constructed. This new collection, referred to as the Dublin Cell Counting (DCC) dataset, is the first of its kind to be made available to the wider computer vision community. State-of-the-art object counting performance is achieved in both the Shanghaitech (parts A and B) and Penguins datasets while competitive performance is observed on the TRANCOS and Modified Bone Marrow (MBM) datasets, all using a shared counting model.