The InterEvDock3 protein docking server exploits the constraints of evolution by multiple means to generate structural models of protein assemblies. The server takes as input either several sequences or 3D structures of proteins known to interact. It returns a set of 10 consensus candidate complexes, together with interface predictions to guide further experimental validation interactively. Three key novelties were implemented in InterEvDock3 to help obtain more reliable models: users can (i) generate template-based structural models of assemblies using close and remote homologs of known 3D structure, detected through an automated search protocol, (ii) select the assembly models most consistent with contact maps from external methods that implement covariation-based contact prediction with or without deep learning and (iii) exploit a novel coevolution-based scoring scheme at atomic level, which leads to significantly higher free docking success rates. The performance of the server was validated on two large free docking benchmark databases, containing respectively 230 unbound targets (Weng dataset) and 812 models of unbound targets (PPI4DOCK dataset). Its effectiveness has also been proven on a number of challenging examples. The InterEvDock3 web interface is available at http://bioserv.rpbs.univ-paris-diderot.fr/services/InterEvDock3/.