The search for sources of high-energy astrophysical neutrinos can be significantly advanced through a multimessenger approach, which seeks to detect the γ-rays that accompany neutrinos as they are produced at their sources. Multimessenger observations have so far provided the first evidence for a neutrino source, illustrated by the joint detection of the flaring blazar TXS 0506+056 in high-energy (E > 1 GeV) and very-high-energy (VHE; E > 100 GeV) γ-rays in coincidence with the high-energy neutrino IceCube-170922A, identified by IceCube. Imaging atmospheric Cherenkov telescopes (IACTs), namely FACT, H.E.S.S., MAGIC, and VERITAS, continue to conduct extensive neutrino target-of-opportunity follow-up programs. These programs have two components: follow-up observations of single astrophysical neutrino candidate events (such as IceCube-170922A), and observation of known γ-ray sources after the identification of a cluster of neutrino events by IceCube. Here we present a comprehensive analysis of follow-up observations of high-energy neutrino events observed by the four IACTs between 2017 September (after the IceCube-170922A event) and 2021 January. Our study found no associations between γ-ray sources and the observed neutrino events. We provide a detailed overview of each neutrino event and its potential counterparts. Furthermore, a joint analysis of all IACT data is included, yielding combined upper limits on the VHE γ-ray flux.