In this paper, we propose Sparse High Rank Adapters (SHiRA) that directly finetune 1-2% of the base model weights while leaving others unchanged, thus, resulting in a highly sparse adapter. This high sparsity incurs no inference overhead, enables rapid switching directly in the fused mode, and significantly reduces concept-loss during multi-adapter fusion. Our extensive experiments on LVMs and LLMs demonstrate that finetuning merely 1-2% parameters in the base model is sufficient for many adapter tasks and significantly outperforms Low Rank Adaptation (LoRA). We also show that SHiRA is orthogonal to advanced LoRA methods such as DoRA and can be easily combined with existing techniques.