I think the best outcome for a Paraguayan offensive is for the planets to align so the Argentine civil wars flare up as they engage the Brazilian armies. And they secure a peace with Brazil by the time Argentina gets its act together and counterattacks. Even then, Paraguay would need to get ready for round two.
Like I said before, paraguay don't have enought population to defeat brazil, even with Argentina in their side
The logic os the war usually goes as: paraguay had more numbers, so they could win
Well, first of all, the paraguyan army was at full mobilization when the war started, almost every able men in the country was at the army, so they simple couldn't replace their losses, they also didn't had enought population left to keep their economy running while at war, there is a joke about the war that is:
A paraguayan officer receives a aidee, who says:
"Sir, we had terrible losses in the last months"
"Who did that? The brazilians?"
"No"
"The argentinians?"
"No"
"don't you say that the uruguayans did that"
"Not, it was the famine and the cold"
The army equipment was also of inferior quality, and their training was also poor, so much that in the battle of Yatay the paraguayans had 1/3 of their forces destroyed, while causing negligible damage on the alliance forces, the same thing repeats in any other battle, as uruguaiana, or the most classic example, Tuyutí.
Another thing is that a demographic and economical desaster was coming to paraguay because of this mobilization, when a citizen is conscripted in the military he's not working, neither having children, or studying, so this lead to a long term decline on their overral economic and populational growth, and if for some ASB reason the paraguayans had won the war, they would have to either demobilize the army, to be counterattacked and suffer the same destiny as OTL, or continue mobilized, dry their economy and collapse, and then be attacked