The newborn duke was named after the Archbishop-Elector of Cologne Maximilian Henry of Bavaria and the "Great" Elector of Brandenburg Frederick William.

In 1684, however, the family agreed to adopt the principle of primogeniture, allowing the entire inheritance to pass to the eldest son and thus preventing further division of the Duchy of Brunswick-Lüneburg into insignificant statelets.

[3] On his eighteenth birthday, his father signed a contract with the Republic of Venice, whereby he sent him to the Morean War as general of Brunswick-Lüneburg troops and nominal commander of 2400 men.

His death made Maximilian William the Duke's second son and prompted him to claim the right to inheritance he had been deprived of in favour of his eldest brother, George Louis.

Maximilian William proceeded to plot to set primogeniture aside, assisted primarily by the Master of the Hunt Joachim von Moltke.

Anthony Ulrich, Duke of Brunswick-Wolfenbüttel, and the prime minister of Brandenburg Eberhard von Danckelmann were also implicated, and it is believed that Duchess Sophia was aware of the conspiracy but did not wish to estrange herself from her younger sons.