There are two good ways to make sure she stays over, better if done at the same time.
1. Build conmfort
2. Make her horny
You can build comfort with rapport and humor.
As far as making her horny, mild c+F can work, as well as kino while on the couch, progress this upwards.
You may ask, how to progress into kino and such. Well I rarely invite women into my apartment unless they know intuitively that I am sexually interested. If she comes in my apartment, kissing and kino are NO problem, because the sub text of our interaction is such that this is a requirement for hanging out with me in my apartment. If it backfires, oh well, I screwed up, you might want to leave, and I forget about this girl until she calls me back. In the meantime I am gaming other girls.