We propose a Bayesian latent space model for clustering longitudinal multilayer networks in which network slices are represented by a finite set of recurrent latent regimes, each associated with a regime-specific latent geometric configuration. Layer-specific hidden Markov chains govern regime membership through a parsimonious additive transition model, allowing heterogeneous temporal dynamics across relational dimensions while sharing a common set of latent configurations. Edge weights are modelled using a Hurdle Negative Binomial distribution, accommodating both excess zeros and overdispersion in weighted networks. An optional sender-receiver extension further captures persistent node-specific heterogeneity. A simulation study demonstrates that the proposed model can accurately recover both latent regimes and their associated configurations, with recovery performance depending on the degree of regimes' similarity. We also assess the robustness of the proposed method under model misspecification. Applications to GDELT geopolitical event and European Parliament roll-call voting data demonstrate the flexibility of the framework across diverse domains.
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