Open-domain dialogue system usually requires different sources of knowledge to generate more informative and evidential responses. However, existing knowledge-grounded dialogue systems either focus on a single knowledge source or overlook the dependency between multiple sources of knowledge, which may result in generating inconsistent or even paradoxical responses. To incorporate multiple knowledge sources and dependencies between them, we propose SAFARI, a novel framework that leverages the exceptional capabilities of large language models (LLMs) in planning, understanding, and incorporating under both supervised and unsupervised settings. Specifically, SAFARI decouples the knowledge grounding into multiple sources and response generation, which allows easy extension to various knowledge sources including the possibility of not using any sources. To study the problem, we construct a personalized knowledge-grounded dialogue dataset \textit{\textbf{K}nowledge \textbf{B}ehind \textbf{P}ersona}~(\textbf{KBP}), which is the first to consider the dependency between persona and implicit knowledge. Experimental results on the KBP dataset demonstrate that the SAFARI framework can effectively produce persona-consistent and knowledge-enhanced responses.