The main task of machine learning is generalization in cases going beyond the cases seen in training. Until recently, the generalization capacity of deep neural networks (DNNs) for homogenization of elastic solids was restricted to microstructure topology only, but for fixed elastic phase parameters. The same is true for related problems aiming at predictions of effective permeabilities, conductivities, and alike. This bottleneck narrows down the range of applications and requires a re-training for any change in the physical properties of individual constituents, which is expensive, cumbersome and, as it turns out, not necessary. The present contribution proposes solutions, how suchlike restrictions can be overcome. Two novel architectures of homogenization-DNNs are introduced, one as a CNN with a two-channel input [1], the other as a hybrid DNN. They both enable predictions for a large variety of microstructures, for arbitrary phase-fractions, and as the key novelty, for almost arbitrary elastic phase properties. Moreover, sharp bounds for periodic boundary conditions are part of the predictions, thereby reducing the uncertainty of the true stiffness of random heterogeneous, non-periodic microstructures. As a result, the generalization capacity of homogenization DNNs is expanded by the dimension of elastic phase properties which enables universal predictions of elasticity tensors in homogenization for heterogeneous materials in their linear elastic regime. References [1] Eidel B. Deep CNNs as universal predictors of elasticity tensors in homogenization. Computer Methods in Applied Mechanics and Engineering, Vol. 403, 115741, 2023.