DS (5 months) usually wakes at least 3 times during the night - often more frequently. He normally has a bottle around 1am and another around 5am. DS is 99th percentile and a little pudgy. I can't help thinking the feeds are more habit than hunger but I can't stand the thought of letting him starve.
A work colleague told me she just cut out the night feeds for her DS at a similar age and only offered water. Apparently, her DC complained for a few nights then started sleeping through.
His night feeding times are totally normal if not quite good for a 5 month old to be honest. The one thing you could try (if you're not doing this already) is a dreamfeed (i.e. feed them while they're half asleep) at 11.30 to try and cut out that 1am feed. There's always the danger he'll change the second feed to 4am though!
I would not advise you to do any form of sleep training before 6 months and certainly wouldn't offer water instead of milk unless they were toddlers to be honest. Give it a month or until you've introduced solids and see where you are, you might find the 1am feed has gone anyway. If you wait till 6 months it gives you the confidence that many babies of that age do not nutritionally require feeding at night time (I always take this to mean between 12 and 5 btw).