Someone other than Andrássy is the Hungarian PM in 1870. Perhaps Deák never stands down, and assumes the mantle himself, as was expected. Andrássy vigorously fought against the idea of an Austria-Hungarian intervention in the Franco-Prussian War, believing that it was no interest of the Magyars whether or not the Hapsburgs regained their position among the German states. Whether or not that is true, a (victorious) war would have brought the Austrians and Hungarians closer together, and would have validated the reasoning behind allowing the Magyars their autonomy. Lets remember that the Compromise was originally envisioned as a temporary settlement, and the ten year renegotiations only led to a continual cycle of constitutional crises. In the aftermath of a Prussian defeat the Hungarians would have 'earned' their special position within the empire, and would ease tensions on both sides.
Short of that, you'd need to avert the Compromise altogether to better increase the efficiency of the Hapsburg state. IOTL the Compromise combined the worst of both Hapsburg absolutism and Hungarian secessionism.