Current methods based on deep learning for self-supervised low-dose CT (LDCT) reconstruction, while reducing the dependence on paired data, face the problem of significantly decreased generalization when training with single-dose data and extending to other doses. To enable dose-extensive generalization using only single-dose projection data for training, this work proposes a novel method of Extendable GENeraLization self-supervised Diffusion (EGenDiff) for low-dose CT reconstruction. Specifically, a contextual subdata self-enhancing similarity strategy is designed to provide an initial prior for the subsequent progress. During training, the initial prior is used to combine knowledge distillation with a deep combination of latent diffusion models for optimizing image details. On the stage of inference, the pixel-wise self-correcting fusion technique is proposed for data fidelity enhancement, resulting in extensive generalization of higher and lower doses or even unseen doses. EGenDiff requires only LDCT projection data for training and testing. Comprehensive evaluation on benchmark datasets, clinical data, photon counting CT data, and across all three anatomical planes (transverse, coronal, and sagittal) demonstrates that EGenDiff enables extendable generalization multi-dose, yielding reconstructions that consistently outperform leading existing methods.