The interactions between solitoffs are extensively investigated. Besides the known solitoff fission and fusion interac- tions, two new types of solitoff interactions are discovered, named the solitoff reconnection and the solitoff annihilation. Taking the asymmetric Nizhnik-Novikov Veselov equation as an illustrative system, five types of solitoff interactions are graphically revealed on the basis of the analytical solution obtained by the modified tanh function expansion method.