Frequency combs are multimode photonic systems that underlie countless precision sensing and metrology applications. Since their invention over two decades ago, numerous efforts have pushed frequency combs to broader bandwidths and more stable operation. More recently, quantum squeezing and entanglement have been explored in single-comb systems for continuous-variable quantum computing and quantum-enhanced spectroscopy. However, the production of bright quantum light across multiple nondegenerate pulses or frequency combs, a key technology for multispectral applications, remains largely unexplored. In this work, we explore a mechanism that generates a series of nonlinearly coupled bright frequency combs through cascaded three-wave upconversion and downconversion processes mediated by a single idler comb. We consider both discrete combs and broadband ultrafast pulse systems, showing how these systems generate inter- and intracomb two-mode squeezing and entanglement directly in the frequency basis, spanning a large spectral range. Furthermore, we demonstrate how these systems can be engineered to produce target cluster states and concentrated two-mode squeezing through covariance matrix optimization. Our findings uncover a new multimode quantum regime enabled by hierarchical nonlinear interactions in two frequency dimensions, unlocking applications such as entanglement-assisted spectroscopy, squeezing-enhanced pump-probe measurements, quantum spectral multiplexing, and spectrally addressable cluster state generation for quantum information science.