AHC: Peruvian Conquest of the Philippines

I don't know why this thought occurred to me, and it might be considered frivolous, but I hope it might generate some discussion on its own merits.

Peru was Spain's most loyal colony in the Americas, but like most of Latin America it has a troubled post-colonial history. The challenge here is to make Peru a powerhouse in its own right (maybe not Great Power levels if that's impossible, but nothing to sniff at either), enough that it can project power into the Pacific, and, eventually, perhaps join a war akin to the Spanish-American War and seize the Philippines for itself as an Asian colony (or, as an integral part of the Peruvian state, whatever's clever).

I'm not even entirely sure what inspired this. The Peruvian state itself doesn't have to be just Peru, either, I would accept various iterations of Peru-Bolivia, some kind of South American superstate (as long as the capital is in Peru proper), or some kind of union between Peru and Chile. The only caveat is that it must be an ex-Spanish state.
 
Maybe Chile has a better shot at this, as after the war of the Pacific, they had the most powerful navy in the (Eastern?) Pacific Ocean. But why would they?
 
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