Good morning Tippy, Three layers is a lot. I would not assume the other layers are still holding to the layer beneath it. I would at least take a couple off. The reason , I would put down new underlayment, 1/4" sheets. There is a difference between underlayment and sub-floor. Be sure to use the proper nails ,[ ringshank ] ,to nail the underlayment. Your new floor will hold , look, and feel better. Another reason to take a couple of layers off is to reduce the floor height. Sure hope I helped, Ron J.