Deep subspace clustering (DSC) networks based on the self-expressive model learn a representation matrix, typically implemented using a fully connected network, in the embedded space. After the learning is complete, the representation matrix is used by the spectral clustering module to assign labels to clusters. However, this approach ignores complementary information present in other layers of the encoder, including the input data. In this paper, we apply a selected linear subspace clustering algorithm to learn representation matrices from the representations obtained by all layers of the encoder network, including the input data. Subsequently, we construct a multilayer graph that integrates information from the graph Laplacians of all utilized layers in a multi-view-like manner, thereby enhancing the performance of the chosen DSC network. Additionally, we provide a formulation of our method for clustering out-of-sample data points. We validate the proposed approach on four well-known datasets using two DSC networks as baseline models. In nearly all cases, the proposed approach achieved statistically significant improvements in three performance metrics. The MATLAB code for the proposed algorithm is available at https://github.com/lovro-sinda/MLG-DSC .