Personal and private Web archives are proliferating due to the increase in the tools to create them and the realization that Internet Archive and other public Web archives are unable to capture personalized (e.g., Facebook) and private (e.g., banking) Web pages. We introduce a framework to mitigate issues of aggregation in private, personal, and public Web archives without compromising potential sensitive information contained in private captures. We amend Memento syntax and semantics to allow TimeMap enrichment to account for additional attributes to be expressed inclusive of the requirements for dereferencing private Web archive captures. We provide a method to involve the user further in the negotiation of archival captures in dimensions beyond time. We introduce a model for archival querying precedence and short-circuiting, as needed when aggregating private and personal Web archive captures with those from public Web archives through Memento. Negotiation of this sort is novel to Web archiving and allows for the more seamless aggregation of various types of Web archives to convey a more accurate picture of the past Web.