Can I book a large group on the same flight through the flight booking API?

Not usually, and it is worth knowing that before you quote a group, because most flight booking APIs are built for ordinary bookings rather than group travel. Airlines normally cap how many passengers can sit in one booking, and beyond that cap the search either comes back empty or the group has to be split.

There is a second reason. An API books at the fare that is on sale at that moment, and airlines release only a limited number of seats at each fare level. So a large party can end up spread across different fare levels, with the later passengers costing more than the first ones, which is awkward when you have already given the customer a single figure for everyone.

For a genuine group, airlines run a separate group desk that quotes one fare for the whole party, usually with a deposit, a deadline for the passenger names and its own change rules. That is arranged directly with the airline rather than through the API. Once the group is confirmed you can normally record it in your travel agency software so it sits with the rest of your bookings and your customer receives the same documents as everyone else.

What the API does handle well is a smaller party, or a large one broken into several bookings, which also suits travellers who want to pay separately. Ask your supplier how many passengers they allow in one booking, and for anything above that speak to the airline's group desk before you give your customer a price.