[373-15] Please you, further, means Please you, tell me further.
[373-16] Manage means management.
[373-17] Signiories is a name for principalities.
[373-18] Prime means first or leading.
[374-19] Who is used for whom, as it was not considered ungrammatical in Shakespeare’s day.
[374-20] Trash means check or set back.
[374-21] Over-topping means rising too high. Prospero means that his brother knew what persons to check when they tried to rise too high, to gain too much power.
[374-22] The brother understood the key that kept officer and office in tune, and so set the minds of all Prospero’s subjects thinking as the usurper wished. That is, Antonio took Prospero’s friends away from him.
[374-23] We would say so that instead of merely that.
[374-24] To closeness means to privacy, to studies in his own home.