As a student pianist for several years, I have been finding it hard for me to resist working separately on some certain works. Noting this, having another "teacher" unlegitimately as one's self would have different reactions as responses from different people. A teacher may be pleased at the enthusiasm of the student to work on their own; nevertheless, do not forget that ther is the repertoire, which the student must work on, and so such a thing may receive negative response. To take the meaning of the OP's question more literally, I personally would never consider having two teachers, as this would be a sort of indication, in my opinion, that one teacher does not have the ability nor the resources to teach me well or thoroughly, even though this may not be true. If this were to ever be true, then I would consider switching teachers completely. Even so, maybe the OP's student does not see the situation in this view, depending on their age. I think there is little that can be done by each teacher than to continue to provide the best musical education each teacher can.
thanks all for useful and comperehensive replies.my primary interest is and will be classical music forever.but my second interest is some kind of pop music. I want to uderstand it.may be they have some tricks to be used for my piano playing,