Large Language Models have demonstrated superior reasoning capabilities by generating step-by-step reasoning in natural language before deriving the final answer. Recently, Geiping et al. introduced 3.5B-Huginn as an alternative to this paradigm, a depth-recurrent Transformer that increases computational depth per token by reusing a recurrent block in latent space. Despite its performance gains with increasing recurrences, this approach is inadequate for tasks demanding exploration and adaptivity, a limitation arising from its single, chain-like propagation mechanism. To address this, we propose a novel dynamic multi-branches routing approach for Huginn, termed as Mixture-of-Depth-Recurrent (MoDr) Transformer, which enables effective exploration of the solution space by shifting linear latent reasoning into a LoRA-based multi-branch dynamic relay mode with a learnable hard-gate routing. Meanwhile, we introduce an auxiliary-loss-free load balancing strategy to mitigate the potential routing collapse. Our empirical results reveal that MoDr achieves average accuracy improvements of +7.2% and +2.48% over the original Huginn model and its fine-tuned variant, respectively, across various mathematical reasoning benchmarks and improvements of +21.21% and +1.52% on commonsense reasoning benchmarks.