Maybe Argentina and Brazil actually get into a shooting war (IIRC they came pretty close to doing that IOTL) over whether Argentina gets Gran Chaco or to divide up Paraguay. Such a war would almost certainly see a large amount of combat in Paraguayan territory, and thus magnify the consequences and damages of the war in Paraguay.
That was quite possible, there were some threats of war, but they never passed from this, basically because no one wanted to have other great war just after the Tripple Alliance War. You would need something much serious to happen to allow it.
Personally, I think that even if Brazil completely disliked the idea of giving to Argentina all the right side of the Paraguay River the Empire could live with that. Paraguay would be even more paranoid about a possible (even if unlikely) annexation and would depend even more on Brazilian support.
Maybe the nation is completely absorbed (why did this not happen, btw?)?
Well, at the beggining the Brazilian diplomats more or less accepted the idea of giving Paraguay to Argentina. The original treaty of alliance recognized the independence of Paraguay
for five years after the end of war, and didn't mention what would happen later. Rufino de Elizalde, the Argentine Foreign Minister, even told the British ambassador, Edward Thornton, that he hoped to live enough to see Bolivia, Paraguay and Argentina joined in one single confederation (of course, it was just a dream).
What was agreed at first is that Argentina would get all the territories in the right side of the Paraguay River until the border with Brazil and the territory of Missiones (the one in dispute with Paraguay, the part disputed with Brazil should be solved later), while Brazil would have a border on the Apa and Igurei rivers. However, the Paraguayan invasion of Mato Grosso was so easy that the Brazilians started to think is it would be wise to give access to all the right side of the Paraguay River to Argentina, because it would give them a good position to invade Mato Grosso if they wanted. So, after the war, Brazil decided to support Paraguay and have the Argentine-Paraguayan border on the Pilcomayo. We have made a very small concession to Paraguay, accepting the border on the hills north of the Igurei River instead of the river itself.
However, if the war had ended faster, with a less successful Paraguayan invasion of Mato Grosso, and hopely with Mitre still as the commander of the allied troops, then the distrust between Brazil and Argentina would be much smaller, and the Argentines would probably get the entire right side of the Paraguay River withou Brazilian complain (and the Brazilian border would be on the Igurei River). Less people would die, but more lands would be lost.
There is also an interesting fact about further Brazilian claims in Paraguay. When the treaty giving the right side of the Paraguay River to Argentina was presented to the Brazilian Parliament, the MPs complained that we were giving them too much, and if that could not be change than Brazil should ask more lands. Some proposed a border on the Aquidaban River, while others even suggested to put the border on the Ypane Guazu (what would make Concepcion, the greatest city of Northern Paraguay, be in Brazilian territory).
Here is a map of Paraguay in 1875. In this map, all the right side of the Paraguay River is considered Argentine territory. The number 1, the green line, shows the possible Brazilian-Paraguayan border on the Aquidaban River. The number 2, the blue one, is the idea of a border on the Ypane Guazu. And the orange line, number three, is the Igurei River, were was the border according to the Brazilian claim before the war.