In BROS, its the retrocession of the Gadsden Purchase
Fascinating. So what could you see Mexico gain in a victory scenario? Depending on the amount of troops they would commit, I'm assuming it would have be substantial Sq milage in Arizona, New Mexico, or California.
In BROS, its the retrocession of the Gadsden Purchase (~30,000 square miles of what was then the New Mexico Territory, today southern Arizona and southwestern New Mexico) which had been purchased in 1853 by the US for $15 million. The goal was to acquire the Mesilla Valley for a southern transcontinental railroad, and was pushed through during the Pierce administration (Santa Anna was the Mexican head of state at the time who signed off on it) for the benefit of the southern Democrats.
By 1862, the American hold is less than a decade old, the area is populated largely by American citizens of Mexican ancestry who were naturalized at the time of the purchase, and it represents the worst of antebellum doughface politics. In BROS, Lincoln and Juarez are fighting their respective wars against European imperialists alligned with local conservative rebels, and so the retrocession (midwifed by Seward as secretary of state) functions to strengthen Juarez against the Mexican Conservatives and is part of a larger deal with the French where - after being defeated at Puebla, and before they (historically) reinforced failure - the US offers to pay off Mexico's debt to France in return for French withdrawal; the Mexicans get the Purchase retrocession and in return, the French and Mexicans open various Mexican ports to neutral flag vessels transhipping various useful cargos to the US overland, including Guaymas on the Pacific coast.
The Mexicans also set up what amounts to a "deniable" force in northeastern Mexico under Carbajal, Cortina, Diaz, and a reconciled Miramon to raid into Texas in 1863, using "captured" French weapons and alongside the Texas Unionists (whose numbers have been bolstered by an anabasis led by Sam Houston). This opens up a second front against the Texans, and along with the Comanche (whose raids have been tacitly encouraged by the US, in the person of Col. Christopher Carson, USV) basically require the Texans to withdraw significant forces from the rebel command in Arkansas, which speeds up Curtis' campaign in Arkansas north of the Arkansas River, which sets the stage for Grant and company to move east across the Mississippi against JE Johnston's westernmost bastion, Fort Pillow and Memphis in Tennessee.
See below for a map of the Purchase.
Best,