How does doubling the concentration of nucleophile affect the rate of a reaction with an SN1 mechanism?
SN1 reactions are stepwise mechanisms that are well-represented by this rate law,
This is because their rate determining step is the first step, and in the first step of SN1, the leaving group is lost and a carbocation intermediate (that seeks stability via arrangements, if possible), occurs.
So, due to the preceding reasoning, increasing the concentration of the nucleophile won't appreciably affect the rate. However, increasing the concentration of the leaving group will.