I've split my party into 2 separate reservations, one right after the other. I usually skip a row or two when choosing seats so that if someone else is online booking at the same time, my party will still be able to sit together
IF you are told there are no group discounts. Try pricing out one ticket at a time. More than likely that many tickets purchased online at one time off an airline's website will bump you up to a higher fare class. If need be, book one adult with one child + the spare .
My dh and I learned the lesson the hard way using miles, there were miles for two tickets, but when we added the third, the miles required then jumped. It will work the same way for fares because there are only "x" number of fares available in each fare class. Normally the lowest priced fare classes sell out first. Just think of it as a bucket filled with groups of different colored balls. Each ball represents a seat and there are only so many balls for each color. There may only be 4 tickets at the lowest price, 2 at the next fare price (class) etc.