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In modern analysis pipelines, Einstein-Boltzmann Solvers (EBSs) are an invaluable tool for obtaining CMB and matter power spectra. To accelerate the computation of these observables, the CosmicNet strategy is to replace the bottleneck of an EBS, which is the integration of a system of differential equations for linear cosmological perturbations, by neural networks. This strategy offers advantages compared to the direct emulation of the final observables, including small networks that are easy to train in high-dimensional parameter spaces, and which do not depend by on primordial spectrum parameters nor observation-related quantities such as selection functions. In this second CosmicNet paper, we present a more efficient set of networks that are already trained for extended cosmologies beyond LCDM, with massive neutrinos, extra relativistic degrees of freedom, spatial curvature, and dynamical dark energy. We release a new branch of the CLASS code, called CLASSNET, which automatically uses networks within a region of trusted accuracy. We demonstrate the accuracy and performance of CLASSNET by presenting parameter inference runs from Planck, BAO and supernovae data, performed with CLASSNET and the COBAYA inference package. We have eliminated the perturbation module as a bottleneck of the EBS, with a speedup that is even more remarkable in extended cosmologies, where the usual approach would have been more expensive while the network's performance remains the same. We obtain a speedup factor of order 150 for the emulated perturbation module of CLASS. For the whole code, this translates into an overall speedup factor of order 3 when computing CMB harmonic spectra (now dominated by the highly parallelizable and further optimizable line-of-sight integration), and of order 50 when computing matter power spectra (less than 0.1 seconds even in extended cosmologies).