Multifocal plane microscopy (MUM) can be used to visualize biological samples in three dimensions over large axial depths and provides for the high axial localization accuracy that is needed in applications such as the three-dimensional tracking of single particles and super-resolution microscopy. This report analyzes the performance of intensity-based axial localization approaches as applied to MUM data using Fisher information calculations. In addition, a new non-parametric intensity-based axial location estimation method, Multi-Intensity Lookup Algorithm (MILA), is introduced that, unlike typical intensity-based methods that make use of a single intensity value per data image, utilizes multiple intensity values per data image in determining the axial location of a point source. MILA is shown to be robust against potential bias induced by differences in the sub-pixel location of the imaged point source. The method's effectiveness on experimental data is also evaluated.