Domain Incremental Learning (DIL) is a continual learning sub-branch that aims to address never-ending arrivals of new domains without catastrophic forgetting problems. Despite the advent of parameter-efficient fine-tuning (PEFT) approaches, existing works create task-specific LoRAs overlooking shared knowledge across tasks. Inaccurate selection of task-specific LORAs during inference results in significant drops in accuracy, while existing works rely on linear or prototype-based classifiers, which have suboptimal generalization powers. Our paper proposes continual knowledge consolidation low rank adaptation (CONEC-LoRA) addressing the DIL problems. CONEC-LoRA is developed from consolidations between task-shared LORA to extract common knowledge and task-specific LORA to embrace domain-specific knowledge. Unlike existing approaches, CONEC-LoRA integrates the concept of a stochastic classifier whose parameters are sampled from a distribution, thus enhancing the likelihood of correct classifications. Last but not least, an auxiliary network is deployed to optimally predict the task-specific LoRAs for inferences and implements the concept of a different-depth network structure in which every layer is connected with a local classifier to take advantage of intermediate representations. This module integrates the ball-generator loss and transformation module to address the synthetic sample bias problem. Our rigorous experiments demonstrate the advantage of CONEC-LoRA over prior arts in 4 popular benchmark problems with over 5% margins.