Perhaps Shakespeare gave Hamlet at least three reasons for feeling "extraordinary grief" because the playwright realized that one by itself was not sufficient reason. Hamlet is still grieving over the death of his father. This can be an intensely traumatic, life-changing experience for a young man. It means the loss of a person he loved and admired. It also means a turning point in the young man's life experience. Now he has to take his father's place. No doubt Hamlet has mixed feelings about his father's death.
Those who have never had a father can at any rate never know the sweets of losing one. To most men the death of a father is a new lease of life. -Samuel Butler
Who doesn’t desire his father’s death? -Fedor Dostoevski
Then, of course, there is the Oedipus theme. If Hamlet had an unconscious Freudian wish to kill his father and marry his mother, then how must he feel when he finds out that his uncle has already married her?
Another reason Hamlet may be experiencing such "extraordinary grief" is that Hamlet, understandably, feels he has been cheated out of his right to inherit his father's throne. A third reason is that he feels, as he clearly shows in his turbulent interview with Gertrude in Act 3, Scene 4, that he is disgusted with his mother's "o're hasty" marriage to his uncle and her licentious behavior with Claudius ever since.
Nay, but to live
In the rank sweat of an enseamed bed,
Stew'd in corruption, honeying and making love
Over the nasty sty!
If these three things were not sufficient reason for Hamlet's "extraordinary grief," compounded as it is with other strong emotions, then by the end of Act 1 he learns that his father was murdered and that it is his duty to kill his uncle in revenge. Shakespeare seems to have taken care to provide Hamlet with many strong reasons to explain his feelings and his motivation.