My kids used to do this. Honestly, I think asking for food had become a habit, rather than a need. If they could go 3-4 hours between nursing as EBF infants, eating a total of 4 times a day, without a fuss, they can do it now on table food
I finally put my foot down and we eat four times a day, total. Breakfast at 7:00, lunch at 11:00, snack at 2:30, supper at 6:00. Kitchen is closed the rest of the time. They (usually) don't even ask anymore, unless I start caving, then they totally revert back. I can't believe how much food they will eat at a meal now that I insist on this. And how much healthier. They devour their vegetables.
They can eat as much or as little of anything served that they want, but I will not make different food to suit someone if they don't like what I serve.
We only eat whole foods. Nothing processed. They can have water whenever they want.
When they leave the table, they must ask to be excused and then that is it, no more food until the next meal (we had a lot of wandering around the kitchen prior to that rule).
Holidays and parties are free for all. I don't worry about when they eat or what. We all need a break sometimes