Applies to things, conditions, or statements/theorems. Its use as a philosophical concept is due to Leibniz. Many-worlds interpretation aside, alternate timelines are not compossible, but a possible timeline is a set of compossible peoeple and events. Not all potential solutions to a problem are, however, compossible (though it's not always easy to get executives to understand this). In use since the 1630s, borrowed from Medieval Latin compossibilis, from com-, together/with + possibilis, that may be done, from posse, to be able/have power.
Mansuetude is fully compossible with muliebrity, and don't let her tell you otherwise.