I know a way to infinitely increase your influence with her. If your awareness modifier is high enough, you can use it to increase your influence. There's an option with her to talk about the miraluka homeworld, and if your awareness is high enough you get another option. After that option, you should (if you've spoken to Atton about it) get another option with Atton saying something else about it. She'll mention how he may not be such a fool after all and the conversation ends, you gaining influence. You can repeat it as many times as you like to gain influence. Atleast you can on the Xbox (not sure if it works the same way on the PC).
However, she'll just spill all of her secrets to you if you do. I find that I don't care enough about her to bother with her influence anyways. I end almost every conversation with her claiming my total distrust of her (which ends in her giving me praise. How infuriating!).