Level of Focus in Anapanasati
Yes, once you have reached sufficient level of concentration you may continue on the breath (samatha) or investigate the mind (vipassana). In my own practice I have a preference for reaching the calmest level possible, so I simply stay with breath, but more quietly, gently, less control, just allowing it to be, no more. At the same time, I don't ignore or suppress things as they arise, i just let them arise, fall, arise, fall. In one door, out the other. It's "kind of" a combination of both Calm and Insight.