The brain processes information through multiple layers of neurons, a representationally powerful approach that complicates learning due to the challenge of identifying responsible neurons when errors occur. To tackle this, we introduce a novel framework that bridges key principles of brain-inspired computation, integrating both recurrence—an essential feature of neural dynamics—and structured feedforward processing. Building on this foundation, a multilayer Liquid State Machine is introduced, that is leveraging feedback alignment, a biologically plausible alternative to traditional backpropagation. The recurrent reservoir captures rich temporal dynamics, while the feedforward structure, guided by feedback alignment, extracts dominant features for more efficient representation. By combining these elements, our approach could represent a step forward in neuro-inspired information processing. As validation, the idea is tested on the neuromorphic MNIST dataset, demonstrating the effectiveness of the proposed architecture. Results show that it outperforms the classical single layer Liquid State Machine in terms of accuracy by more than 3%.