Data sharing enables critical advances in many research areas and business applications, but it may lead to inadvertent disclosure of sensitive summary statistics (e.g., means or quantiles). Existing literature only focuses on protecting a single confidential quantity, while in practice, data sharing involves multiple sensitive statistics. We propose a novel framework to define, analyze, and protect multi-secret summary statistics privacy in data sharing. Specifically, we measure the privacy risk of any data release mechanism by the worst-case probability of an attacker successfully inferring summary statistic secrets. Given an attacker's objective spanning from inferring a subset to the entirety of summary statistic secrets, we systematically design and analyze tailored privacy metrics. Defining the distortion as the worst-case distance between the original and released data distribution, we analyze the tradeoff between privacy and distortion. Our contribution also includes designing and analyzing data release mechanisms tailored for different data distributions and secret types. Evaluations on real-world data demonstrate the effectiveness of our mechanisms in practical applications.