Although current PET scanners are designed and optimized to detect double coincidence events, there is a significant amount of triple coincidences in any PET acquisition. Triple coincidences may arise from causes such as: inter-detector scatter (IDS), random triple interactions (RT), or the detection of prompt gamma rays in coincidence with annihilation photons when non-pure positron-emitting radionuclides are used (β(+)γ events). Depending on the data acquisition settings of the PET scanner, these triple events are discarded or processed as a set of double coincidences if the energy of the three detected events is within the scanner's energy window. This latter option introduces noise in the data, as at most, only one of the possible lines-of-response defined by triple interactions corresponds to the line along which the decay occurred. Several novel works have pointed out the possibility of using triple events to increase the sensitivity of PET scanners or to expand PET imaging capabilities by allowing differentiation between radiotracers labeled with non-pure and pure positron-emitting radionuclides. In this work, we extended the Monte Carlo simulator PeneloPET to assess the proportion of triple coincidences in PET acquisitions and to evaluate their possible applications. We validated the results of the simulator against experimental data acquired with a modified version of a commercial preclinical PET/CT scanner, which was enabled to acquire and process triple-coincidence events. We used as figures of merit the energy spectra for double and triple coincidences and the triples-to-doubles ratio for different energy windows and radionuclides. After validation, the simulator was used to predict the relative quantity of triple-coincidence events in two clinical scanners assuming different acquisition settings. Good agreement between simulations and preclinical experiments was found, with differences below 10% for most of the observables considered. For clinical scanners and pure positron emitters, we found that around 10% of the processed double events come from triple coincidences, increasing this ratio substantially for non-pure emitters (around 25% for (124)I and > 50% for (86)Y). For radiotracers labeled with (18)F we found that the relative quantity of IDS events in standard acquisitions is around 18% for the preclinical scanner and between 14 and 22% for the clinical scanners. For non-pure positron emitters like (124)I, we found a β(+)γ triples-to-doubles ratio of 2.5% in the preclinical scanner and of up to 4% in the clinical scanners.