Despite their impressive performance, self-supervised speech models often struggle to generalize to new languages and tend to forget previously acquired knowledge during continual training. To address this, we propose Lamer-SSL, a parameter-efficient framework that integrates a Layer-Aware MixturE of LoRA Experts (Lamer) module with a replay strategy. The Lamer module enables flexible balancing between shared and language-specific representations, while layer-aware expert allocation assigns more experts to deeper layers where semantic information is richer. Meanwhile, the replay strategy retains prior knowledge using minimal data, mitigating forgetting during continual training. Experiments on automatic speech recognition (ASR) and language identification (LID) demonstrate that Lamer-SSL extends self-supervised models to new languages effectively while maintaining strong performance on previously learned languages with only 2.14% parameters being trainable.