We started demand feeding my LO when she was about 2 months old, because she wasn't lasting until the next feed. Everyone assumes that if you start demand feeding, your baby will take more milk, but my LO took less milk, more frequently, so overall, she would have the same amount of milk per day. Looking back, I don't regret starting demand feeding, because my LO is happier now she gets a bottle when she needs it, instead of having to wait until her next feed. A baby doesn't understand why they're crying for milk, but not getting it. IMO if a baby cries for a feed, you should give it.
I wouldn't go onto hungry milk just yet, because if your LO isn't actually that hungry, they will be drinking less ounces to satisfy their hunger, and therefore taking less fluids. You need to ensure your LO stays hydrated. If in a few weeks you still think he may need it, speak to your HV and see what they say. Don't worry if your baby takes a little more than the normal ounces for their age; it will all level out once they get more active.