Can we be both agreeable and disagreeable at the same time?
There are two main theories of behaviour, trait theory and situationism.
What you are referring to is known as situationism. A doyen of trait theory was Raymond Cattell who was the father of modern personality testing (his 16PF test was a forerunner of the Big Five).  An assumption of trait theory is that individuals have inherent personality traits and will therefore behave consistently irrespective of the situation. Conversely, situationists suggest that the situation an individual finds themselves in has a significant impact on the individual's behaviour.  The extremity of the situationist argument is that individual's do not have personality traits at all and that the situation is sufficient to predict and individual's behaviour. Both trait theorists and the situationists have evidence to support their positions and I think it is generally accepted that the truth lies somewhere in the middle. To resolve the trait theory versus situationism argument are the emerging computational approaches such as cybernetics and system dynamics. Unfortunately, these emerging fields are in their infancy and nothing to report at this time.
All of the above was a long-winded and round-about way of saying that the Big Five is not perfect, but probably the best you can do just at the moment.