Is it possible for a sibling to take custody of another sibling?

I am 24 years old. I work full time as well as go to school full time for nursing, I have a stable roof over my head and transportation, no children. I have a younger sister who is 5, she is currently staying at my grandparents house but they have no legal rights at the moment. Sorry for the length. Her biological father who is paying child support right now is a registered sex offender. Our mother has had 5 children, me she gave custody up of to get out of jail. A 15 year old who is with her biological father due to winning custody from our mother. A 11 year old who is with her biological father due to winning custody from out mother as well, and a 6 year old boy who has been adopted by my grandparents due to our mother giving him up for adoption, and the last one, the one I am asking about my mother still has custody of, my mother is a 40 something year old woman whom is in and out of jail about 2 a year for the last 10 years. She has done prostitution, she has been caught selling and doing drugs, severe ones, and has written fraudulent checks as well as robbery and other legal issues. She is still doing drugs and isn’t stopping, she will not give up custody of my sister because she is getting the child support weekly and won’t give that up. She has no job, she has no car, she has no actual roof over her head, they have slept in vehicles. She is an unfit mother needless to say. I want to take custody of Tori from our mother and give her a good life. Is this possible?