Low Rank Adaptation (LoRA)  has gained massive attention in the recent generative AI research. One of the main advantages of LoRA is its ability to be fused with pretrained models adding no overhead during inference. However, from a mobile deployment standpoint, we can either avoid inference overhead in the fused mode but lose the ability to switch adapters rapidly, or suffer significant (up to 30% higher)  inference latency while enabling rapid switching in the unfused mode. LoRA also exhibits concept-loss when multiple adapters are used concurrently. In this paper, we propose Sparse High Rank Adapters (SHiRA) , a new paradigm which incurs no inference overhead, enables rapid switching, and significantly reduces concept-loss. Specifically, SHiRA can be trained by directly tuning only-of the base model weights while leaving others unchanged. This results in a highly sparse adapter which can be switched directly in the fused mode. We further provide theoretical and empirical insights on how high sparsity in SHiRA can aid multi-adapter fusion by reducing concept loss. Our extensive experiments on LVMs and LLMs demonstrate that finetuning only a small fraction of the parameters in the base model is sufficient for many tasks while enabling both rapid switching and multi-adapter fusion. Finally, we provide a latency- and memory-efficient SHiRA implementation based on Parameter-Efficient Finetuning (PEFT)  Library. This implementation trains at nearly the same speed as LoRA while consuming lower peak GPU memory, thus making SHiRA easy to adopt for practical use cases.