Not in the same year. Daffodils should be deadheaded so that the energy produced by the leaves gets stored in the bulbs, to nourish the following year's flowers, rather than being used to produce seeds.
Daffodils bloom in the spring, but there are many different varieties. Some varieties bloom quite early, others bloom mid-season, and still others bloom later. Depending on the weather, I can have daffodils blooming in my garden from early March until early May. There might be some varieties that bloom even later. I just don't have them.
It's possible that breeders are working to develop a reblooming daffodil, but I haven't heard of any that have reached the market yet. I have, however, seen reblooming irises and reblooming daylilies for sale.
"Isn't it enough to see that a garden is beautiful without having to believe that there are fairies at the bottom of it too?" - Douglas Adams