If Alita was any other man or woman, she wouldn't even care about the other. She would take what she wants and leave but Alita was very different. Ivy knew how to surrender when her opponent was stronger than her.
It has always been her dream to be conquered by someone mighty and stronger than she and Alita was the person. So, what if Alita was seeing that small girl Gail and that vixen Clara.
In her world, capable men and women deserve to have many lovers as this showed their mighty. As long as they don't deprive her of what she wants, she will live peacefully with them. this is the reason why she didn't make a move on those two little girls when she heard about them.
After settling the issues at hand, in the following two days, Ivy tagged alongside Alita as Alita kept on buying mountains of stones.