  Terrestrial exoplanets orbiting M-dwarf stars are promising targets for
transmission spectroscopy with existing or near-future instrumentation. The
atmospheric composition of such rocky planets remains an open question,
especially given the high X-ray and ultraviolet flux from their host M dwarfs
that can drive atmospheric escape. The 1.3 $R_\oplus$ exoplanet GJ 486b
($T_{\rm{eq}} \sim$ 700 K), orbiting an M3.5 star, is expected to have one of
the strongest transmission spectroscopy signals among known terrestrial
exoplanets. We observed three transits of GJ 486b using three different
high-resolution spectrographs: IRD on Subaru, IGRINS on Gemini-South, and
SPIRou on the Canada-France-Hawai'i Telescope. We searched for atmospheric
absorption from a wide variety of molecular species via the cross-correlation
method, but did not detect any robust atmospheric signals. Nevertheless, our
observations are sufficiently sensitive to rule out several clear atmospheric
scenarios via injection and recovery tests, and extend comparative
exoplanetology into the terrestrial regime. Our results suggest that GJ 486b
does not possess a clear H$_2$/He-dominated atmosphere, nor a clear 100%
water-vapor atmosphere. Other secondary atmospheres with high mean molecular
weights or H$_2$/He-dominated atmospheres with clouds remain possible. Our
findings provide further evidence suggesting that terrestrial planets orbiting
M-dwarf stars may experience significant atmospheric loss.
