Paraguayan War: What if Paraguay counter-attacked after Battle of Curupayty?

I found out about this battle in the Most one-sided war thread.

OTL, the battle was a complete failure for the Triple Alliance, as they lost 10,000 killed and wounded out of a force of 20,000 against the Paraguayans losing only 23 killed and 79 wounded. The only thing that prevented total disaster for the Triple Alliance was Paraguayan President Francisco Solano Lopez's refusal to order a counter-attack against the defeated and exhausted Brazilian-Argentine army.

So let us presume that Lopez orders General Jose Diaz, the Paraguayan commander in the battle, to counter-attack. With the remaining Triple Alliance forces exhausted and many already starting to flee on their own, the result would probably be an utter rout. What then? Does the Triple Alliance decide to start negotiations, or is the war merely prolonged?
 
Not sure, but it would probably just prolong it. I think the latest opportunity Paraguay had to force the Triple Alliance to the negotiating table was at Tuyuti, the largest battle of the war. I'm not even sure if they really could mount an effective counter-attack since the Paraguayan army was in really poor shape at this point.
 
The Battle of Curupaiti was part of an attempt to flank the Humaitá defences, that had started with the earlier landing at Curuzu(see http://upload.wikimedia.org/wikiped...guai-Operações_Passagem_Humaita_1866-1868.png, from Wikipedia in Portuguese. The main Triple Alliance army still was camped at Tuiuti during the battle.

As for the battle itself, if the Paraguayan forces counter-attack, they have the chance to overrun the Triple Alliance forces, but the Paraguayan forces would expose themselves to bombardment from whichever Brazilian Navy ships were in Curuzu(I don't know if there were any, or if the ships that participated in the bombardment of Curupaiti went back to Curuzu - I suspect the latter).

Assuming the Triple Alliance forces are overrun and destroyed, I think it wouldn't make much difference in the end. The consequences of the defeat at Curupaiti already were large: most Uruguayan and Argentinean forces were removed from the theater of operations, and Caxias became the new C-in-C of the Brazilian Army and the Triple Alliance forces. When he assumed command, he spent almost one year building a logistic tail and training the army.

This thread reminded me of something: When the Triple Alliance took Fort Curuzu, the defences at Curupaiti were virtually abandoned, and, IIRC, there were reports of it being so, by advance scouts. The 19-20 days between the fall of Curuzu Fort and the advance at Curupaiti gave the Paraguayans time to man and expand the defences, which was the reason the Triple Alliance was defeated there.

So, what if the Triple Alliance pressed forward and took Curupaiti soon after Curuzu? The Triple Alliance would keep on encircling Humaitá, but would they take it earlier, or would they be defeated somewhere else with the same consequences of OTL Curupaiti?
 
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