Abstract: In this talk, I will propose a new formula for computing holographic Renyi entropies in the presence of multiple extremal surfaces. The proposal is based on computing the wave function in the basis of fixed-area states and assuming a diagonal approximation for the Renyi entropy that preserves replica symmetry at integer $n$. I will discuss conditions under which the proposal agrees with the existing cosmic brane proposal for holographic Renyi entropy, while in various situations, there can be leading orde corrections to the cosmic brane proposal even far from entanglement phase transitions.