I have no experience with the giants. But I suspect they will set more than one or two fruit if allowed. If in doubt just harvest the little pumpkins and use them as summer squash. The plant will certainly flower again if it is not maturing seed in those potentially crossed fruit.

George
Tahlequah, OK

Generally, if you use the plants as summer squash and continue to harvest the immature fruits, they'll keep producing flowers. This is how zucchini are harvested. They're actually the same species (c. pepo) as sugar pie pumpkins which are allowed to mature fully. If you let the plant go the full reproductive cycle it will shut down flower production once a few fruits have set and are well on their way to development.

your pumpkin will put out more flowers, as long as it is healhy. as the vine grows out they put out more flowers female and males at the base. and some males out on the vine. the plant has to be big enough to support the pumpkin.