In this paper we present a silicon photomultiplier (SiPM) readout system based on a field-programmable gate array (FPGA), which is capable of converting any commercial 16-channel analog SiPM array into a hybrid device with fully-digital readout for application in time of flight positron emission tomography (TOF-PET). In principle this hybrid SiPM array can be implemented with several leading edge discriminators (LEDs) per channel, so that multiple timestamps can be acquired per scintillation pulse allowing to estimate the time of interaction more robustly than if a single timestamp is used. These concepts were studied experimentally in two different ways. In the first approach, we utilized discrete components in combination with an array of time-to-digital converters (TDCs) implemented and validated on the FPGA. The overall resolution of each channel was 56 ps FWHM or better, while crosstalk was undetectable. In the second approach, we utilized a four-channel high-speed acquisition board operating at 5 GSPS and emulated a multiple-LED acquisition by post-processing the digitized waveforms. We present, for the first time, experimental results obtained with the best linear unbiased estimator (BLUE) to estimate the time of interaction from the multiple timestamps.