Third War of Supremacy
In Look to the West, a world war approximately analogous to the OTL Seven Years' War, but lasting for a shorter time, with different causes and some missing participants, and different results.
The war began over Austria and France reaching a rapproachment in the 'Diplomatic Revolution' of 1756, dramatically altering the balance of power in Europe. For that reason, an alternative name for this conflict was the 'War of the Diplomatic Revolution'. Battles were fought worldwide.
In North America, British troops and newly raised regiments from the young Empire of North America successfully took Quebec and Montreal from France.
In India, British East India Company attempts to recover from the losses in the Second War of Supremacy foundered when the Nawab of Bengal turned against the Company. The Company overthrew the Nawab and took direct control of Bengal, but this left the French even more secure in their control of the Carnatic. The French took Cuddalore from the BEIC, ending any prospect of British trade or control in the Carnatic.
In Europe, Prussia finally succumbed after King Frederick II virtually committed suicide at the disastrous Battle of Kunersdorf, after winning many stunning victories against the odds. Prussia was dismembered at the Treaty of Warsaw, the spoils going to Saxony, Poland, Austria, Sweden and Russia. The other German allies of Britain survived more or less status quo ante bellum.
In Africa, France lost Senegal to Britain, thus forming the basis for what would become the Space-Filling Empire.