It's a false assumption to assume that more interviews is going to drive the false positive rate down. Increased volume or difficulty are not the keys to driving the false positive rate down. Better preparation is the key to driving the false positive rate down. Your team has to be crystal clear about what they are looking for in a candidate. That will allow you to create better job descriptions and create better interview questions and processes.

Increasing the difficulty and frequency of interviews is a bandage for bad processes. It's also going to increase your false negative rate. In a job market like this, you just can't afford to do that.