Conventional protein-protein docking algorithms usually rely on heavy candidate sampling and re-ranking, but these steps are time-consuming and hinder applications that require high-throughput complex structure prediction, e.g., structure-based virtual screening. Existing deep learning methods for protein-protein docking, despite being much faster, suffer from low docking success rates. In addition, they simplify the problem to assume no conformational changes within any protein upon binding (rigid docking). This assumption precludes applications when binding-induced conformational changes play a role, such as allosteric inhibition or docking from uncertain unbound model structures. To address these limitations, we present GeoDock, a multi-track iterative transformer network to predict a docked structure from separate docking partners. Unlike deep learning models for protein structure prediction that input multiple sequence alignments (MSAs), GeoDock inputs just the sequences and structures of the docking partners, which suits the tasks when the individual structures are given. GeoDock is flexible at the protein residue level, allowing the prediction of conformational changes upon binding. For a benchmark set of rigid targets, GeoDock obtains a 41% success rate, outperforming all the other tested methods. For a more challenging benchmark set of flexible targets, GeoDock achieves a similar number of top-model successes as the traditional method ClusPro [1], but fewer than ReplicaDock2 [2]. GeoDock attains an average inference speed of under one second on a single GPU, enabling its application in large-scale structure screening. Although binding-induced conformational changes are still a challenge owing to limited training and evaluation data, our architecture sets up the foundation to capture this backbone flexibility. Code and a demonstration Jupyter notebook are available at https://github.com/Graylab/GeoDock.