How do incumbent parties strategize against challengers when a new partisan cleavage cuts across the incumbent's electoral coalition? This article argues that a two-dimensional extension of Riker's anticoordination thesis conflicts with Downsian extensions. It shows that when voters coordinate on a single challenger based on their shared preference on a cross-cutting cleavage, a vote-maximizing incumbent party should move away from the challenger on the primary dimension of competition, even at the risk of abandoning the center. The article develops this hypothesis with reference to dominant parties in competitive authoritarian regimes where challenger parties constantly attempt “heresthetical” moves by mobilizing regime issues into the partisan debate, and it tests the predictions with an original sample survey of national leaders of Mexico's Revolutionary Institutional Party (PRI). It also spells out the implications of the findings for dominant party survivability in democratic transitions and, more broadly, for incumbents' spatial strategies in the face of new partisan cleavages.