Are you talking about connecting the phases of a woofer and a tweeter in a speaker system that has a passive crossover network (filter)?
If the crossover network is two even-order Butterworth filters then if the speakers are in phase there will be a notch at the crossover frequency.
If the speakers have opposite phase then there will be a +3dB boost at the crossover frequency.
Use a Linkwitz-Riley crossover network and the response will be flat when the network has two even-order filters and the speakers are connected with opposite phase.