PHB, page 172:
Multiple Mental Control Effects:
Sometimes magical effects that establish mental control render each other irrelevant. For example, a hold person effect renders any other form of mental control irrelevant because it robs the subject of the ability to move. Mental controls that don’t remove the recipient’s ability to act usually do not interfere with each other.
For example, a person who has received a geas/quest spell can also be subjected to a charm person spell. The charmed person remains committed to fulfilling the quest, however, and resists any order that interferes with that goal. In this case, the geas/quest spell doesn’t negate charm person, but it does reduce its effectiveness, just as nonmagical devotion to a quest would.
If a creature is under the mental control of two or more creatures, it tends to obey each to the best of its ability, and to the extent of the control each effect allows. If the controlled creature receives conflicting orders simultaneously, the competing controllers must make opposed Charisma checks to determine which one the creature obeys.