Time-resolved photon counting methods have a finite bandwidth that restricts the acquisition speed of techniques like fluorescence lifetime imaging microscopy (FLIM). To enable faster imaging, computational methods can be employed to count photons when the output of a detector is directly digitized at a high sampling rate. Here, we present computational photon counting using a hybrid photodetector in conjunction with multithreshold peak detection to count instances where one or more photons arrive at the detector within the detector response time. This method can be used to distinguish up to five photon counts per digitized point, whereas previous demonstrations of computational photon counting on data acquired with photomultiplier tubes have only counted one photon at a time. We demonstrate in both freely moving and a human breast cancer cell line undergoing apoptosis that this novel multithreshold peak detection method can accurately characterize the intensity and fluorescence lifetime of samples producing photon rates up to 223%, higher than previously demonstrated photon counting FLIM systems.