Final answer:
Hamlet is referencing the offenses committed against him that he has the power to control or command.
Step-by-step explanation:
When Hamlet says, 'more offenses at my beck,' he is referring to the actions or offenses committed against him that he has the power to command or control. In this context, Hamlet is expressing his frustration and anger at the various wrongdoings and injustices he has faced.
An example of one such offense would be the murder of his father by his uncle, Claudius. Hamlet feels the weight of this offense and seeks to avenge his father's death, but he is also overwhelmed by the many other offenses and challenges he encounters throughout the play.