There's at least two instances in Deep Space Nine, at least sort of.
In Through The Looking Glass, Sisko-prime was brought to the mirror universe in order to speak to his late wife's counterpart. He was able to use his influence as her husband's counterpart to persuade her to switch sides and join the rebellion.
Memory Alpha summary.
In the "mirror universe," Sisko must persuade the alternate version of his dead wife to join the Terran Rebels, or he will watch her die a second time.
In the episode Resurrection, the mirror counterpart of Kira's dead lover arrives in the prime universe. Again, this is a plot to use his influence to persuade her.
Memory Alpha summary
An alternate version of Vedek Bareil arrives from the "Mirror Universe" seeking refuge.