Parameter-Efficient Fine-Tuning (PEFT) is essential for adapting Large Language Models (LLMs) under resource constraints, yet existing methods often treat initialization and optimization as separate concerns. This paper introduces OLoRA+, a novel hybrid approach that synergistically combines the structural stability of Orthonormal Low-Rank Adaptation (OLoRA) with the accelerated convergence of LoRA+. By initializing adapter matrices via QR decomposition of pre-trained weights and applying differential learning rates to the upstream and downstream projection matrices, OLoRA+ aims to enhance both stability and feature learning speed. We evaluated the method on the LLMs models using a subset of the Alpaca instruction-following dataset. Empirical results demonstrate that OLoRA+ consistently outperforms the standard OLoRA baseline across Evaluation Loss, BLEU, and ROUGE metrics without incurring additional computational costs. Crucially important that our analysis uncovers two distinct effective learning regimes: a ”Refinement” strategy (learning rate ratio λ < 1) that optimizes the initial orthonormal basis, and an ”Exploration” strategy (λ>1) that seeks new parameter directions. These findings suggest that OLoRA+ offers a more versatile and robust framework for efficient LLM adaptation than its predecessors.