Mutually Exclusive
The 7PK paper does not state whether mutually exclusive classification is a goal. The layout does not imply that the same item could have multiple parents. However, there are cases in which items could be classified in multiple ways. Vulncat's language-specific breakdown at the top level reuses the 7PK kingdoms at the next level below the individual languages.
For example, CWE-491 (Public cloneable() Method Without Final (aka 'Object Hijack')) is classified under the "Insufficient Encapsulation" kingdom (CWE-485), but it is also a fairly clear example of another kingdom, "API Abuse" (CWE-227). Path Manipulation (CWE-249) is described as a low-level variant of a buffer overflow (CWE-120), and it is in the same Input Validation kingdom; however, CWE-251 (Often Misused: String Management) also identifies the risk of string manipulation functions that enable buffer overflows, but it is classified under CWE-227 (API Abuse) instead. The rationale for these classification choices is not immediately clear.
CWE-699 does not aim to be mutually exclusive. Instead, it uses diverse categories with many relationships. However, as explained previously, this has implications for repeatability.