Existing parameter-efficient fine-tuning (PEFT) methods for large language models (LLMs), such as LoRA and PiSSA, constrain model updates to low-rank subspaces, limiting their expressiveness and leading to suboptimal performance on complex tasks. To address this, we introduce **H**igh-rank **D**istributed **PiSSA (HD-PiSSA)**, a distributed PEFT approach that initializes **orthogonal adapters** across different devices and aggregates their delta updates collectively on (W) for fine-tuning. Unlike Data Parallel LoRA or PiSSA, which maintain identical adapters across all devices, HD-PiSSA assigns different principal components of the pre-trained weights to each GPU, significantly expanding the range of update directions. This results in over 16× higher effective updated ranks than data-parallel LoRA or PiSSA when fine-tuning on 8 GPUs with the same per-device adapter rank. Empirically, HD-PiSSA benefits from this extra optimization flexibility and outperforms both LoRA and PiSSA across a variety of challenging downstream tasks, including mathematics, code, and multi-task learning.