How does Cassio exploit three women in Act 3 Scene 4 of Othello?
In Act III.iv of Othello, Cassio uses Desdemona and exploits only Bianca. He has no real relationship with Emelia.
Cassio cares more about his lost reputation than he does about the reputation of women. To him, as it was for most men of the time, women are second-class citizens, far down on the social ladder. Ironically, since Cassio has lost his reputation, he has joined the women in status: he's as far down the ladder as they are, maybe lower. As a result, Cassio appeals to Desdemona to act as a go-between to help him regain favor in Othello's eyes. Honestly, this is immature, if not pandering. He uses, if not exploits, Desdemona's virtue for his own purposes:
I do bessech you / That by your virtuous means I may again / Exist, and be a member of his love / Whom I, with all the office of my heart, Entirely honor.
Cassio is not as naive as she; he should know that Desdemona's appeal might very well anger Othello and make him jealous. He appeals to her anyway; he intentionally puts her reputation at stake to save his own. Cassio resents his status as equal to women; therefore, he uses the best of the women to help him move toward again becoming superior to them.
As for Bianca, Cassio exploits her for pleasure. She is his courtesean, and his speech toward her is rather sexist. He calls her his sweetheart and acts impatiently toward her:
Go to, woman! / Throw your vild guesses in the devil's teeth, / From whence you have them. You are jealious now...
Cassio exhibits the classic male double standard: he may be jealous of Othello's reputation, but Bianca may not be jealous of another woman's. Later, he uses understatement (litote) to placate her. He says that he "doesn't not love her" as a clever way of keeping her around for his sexual purpose:
Not that I love you not.
He uses the handkerchief in the same way, as a means of keeping her.
In Act 3 Scene 4 of Othello, Desdemona realizes that Othello is angry with her about losing the handkerchief. Emilia is by her side when Othello insists that she find it. Shortly afterwards, Desdemona and Emilia run into Cassio and he asks Desdemona to speak to Othello on his behalf. Cassio claims his love and loyalty for Othello and cannot understand why Othello is cross with him. Desdemona says that she is currently at odds with her husband but that she will indeed speak to Othello on Cassio's behalf. Once Desdemona and Emilia exit the scene, Bianca enters and it is revealed that Cassio has been away from her for a week. To appease her, Cassio gives her the handkerchief. Bianca thinks that he has gotten it from a mistress, but he corrects her false impressions.
Reviewing the scene, I think the word "exploit" is rather strong. Cassio makes appeals to the women for his own benefit, but he is not exploiting them.