Continually updating model-based indexes in generative retrieval with new documents remains challenging, as full retraining is computationally expensive and impractical under resource constraints. We propose MixLoRA-DSI, a novel framework that combines an expandable mixture of Low-Rank Adaptation experts with a layer-wise out-of-distribution (OOD)-driven expansion strategy. Instead of allocating new experts for each new corpus, our proposed expansion strategy enables sublinear parameter growth by selectively introducing new experts only when significant number of OOD documents are detected. Experiments on NQ320k and MS MARCO Passage demonstrate that MixLoRA-DSI outperforms full-model update baselines, with minimal parameter overhead and substantially lower training costs.