  In the quest for high-energy neutrino sources, the Astrophysical
Multimessenger Observatory Network (AMON) has implemented a new search by
combining data from the High Altitude Water Cherenkov (HAWC) observatory and
the Astronomy with a Neutrino Telescope and Abyss environmental RESearch
(ANTARES) neutrino telescope. Using the same analysis strategy as in a previous
detector combination of HAWC and IceCube data, we perform a search for
coincidences in HAWC and ANTARES events that are below the threshold for
sending public alerts in each individual detector. Data were collected between
July 2015 and February 2020 with a livetime of 4.39 years. Over this time
period, 3 coincident events with an estimated false-alarm rate of $< 1$
coincidence per year were found. This number is consistent with background
expectations.
