As an approach to all-digital positron emission tomography (PET) that extracts both energy and time-of-flight resolution (TOFPET), we have built two channels of a multithreshold discriminator, each with up to 8 independent thresholds that can be set externally. The extraction of event timing and energy can be done using the digitized times of the leading and trailing edge-crossings of a signal for each of the thresholds, measured using the CERN HPTDC. Two Hamamatsu R9800 photomultiplier tubes (PMTs) coupled with LSO crystals (6.25mm x 6.25mm x 25mm) were spaced 4.5cm apart, and a Na-22 positron source was placed approximately in the middle of the two PMTs. Each signal was fed into a multi-threshold channel, and the timing information from the leading and trailing edge transitions of 4 of the thresholds per PMT were read out by a Tektronix TDS6154C oscilloscope at 20 GHz. The event timing was determined using 1, 2, 3, and 4 thresholds. Using a linear fit to the crossing times from 3 thresholds and comparing to the oscilloscope sampling, we find that the use of three thresholds contributes an additional 52 ps (FWHM) to the single-channel timing resolution. Using 2 thresholds, the time resolution on the coincidence between the two crystals was measured to be 341 ps (FWHM). The pulse shape also was reconstructed based on the timing of falling edges, with a reconstructed 18% energy resolution (FWHM), compared to 13% obtained with the oscilloscope sampling. Details of the results on the timing and energy resolutions by using the multi-threshold method indicate that it is a promising approach for all-digital PET.