Fast, accurate, deformable image registration is an important aspect of image-guided interventions. Among the factors that can confound registration is the presence of additional material in the intraoperative image - e.g., contrast bolus or a surgical implant - that was not present in the prior image. Existing deformable registration methods generally fail to account for tissue excised between image acquisitions and typically simply "move" voxels within the images with no ability to account for tissue that is removed or introduced between scans. We present a variant of the Demons algorithm to accommodate such content mismatch. The approach combines segmentation of mismatched content with deformable registration featuring an extra pseudo-spatial dimension representing a reservoir from which material can be drawn into the registered image. Previous work tested the registration method in the presence of tissue excision ("missing tissue"). The current paper tests the method in the presence of additional material in the target image and presents a general method by which either missing or additional material can be accommodated. The method was tested in phantom studies, simulations, and cadaver models in the context of intraoperative cone-beam CT with three examples of content mismatch: a variable-diameter bolus (contrast injection); surgical device (rod), and additional material (bone cement). Registration accuracy was assessed in terms of difference images and normalized cross correlation (NCC). We identify the difficulties that traditional registration algorithms encounter when faced with content mismatch and evaluate the ability of the proposed method to overcome these challenges.