if the vector sum of the force applied by you and the force applied by another person is zero, then the object will not accelerate since the net force on the object is zero in this case. hence the object will not move at all or if it was already moving , will move at constant velocity.
if the vector sum of the force applied by you and the force applied by another person is non-zero, then the object will not accelerate since there is net force on the object in this case. hence the object will accelerate.