  Networks incorporating higher-order interactions are increasingly recognized
for their ability to introduce novel dynamics into various processes, including
synchronization. Previous studies on synchronization within multilayer networks
have often been limited to specific models, such as the Kuramoto model, or have
focused solely on higher-order interactions within individual layers. Here, we
present a comprehensive framework for investigating synchronization,
particularly global synchronization, in multilayer networks with higher-order
interactions. Our framework considers interactions beyond pairwise connections,
both within and across layers. We demonstrate the existence of a stable global
synchronous state, with a condition resembling the master stability function,
contingent on the choice of coupling functions. Our theoretical findings are
supported by simulations using Hindmarsh-Rose neuronal and R\"{o}ssler
oscillators. These simulations illustrate how synchronization is facilitated by
higher-order interactions, both within and across layers, highlighting the
advantages over scenarios involving interactions within single layers.
