We report on the analysis of a multiphase Lyman limit system (LLS) at z = 0.39047 identified toward the background quasar FBQS J0209–0438. The O VI doublet lines associated with this absorber have a different profile from the low-ionization metals and H i. Ly α has a very broad H i (b ≈ 150 km s−1) component well-aligned with one of the O VI components. The Doppler b-parameters for the broad H i and O VI indicate gas with T = (0.8 − 2.0) × 106 K and a total hydrogen column density that is an order of magnitude larger than the cooler phase of gas responsible for the LLS. Observations by the Very Large Telescope MUSE show two moderately star-forming galaxies within ρ ≲ 105 kpc and ∣Δv∣ ≲ 130 km s−1 of the absorber, one of them a dwarf galaxy (M * ≈ 106 M ⊙) overlapping with the quasar point-spread function, and the other a larger galaxy (R 1/2 ≈ 4 kpc) with M * ≈ 3 × 1010 M ⊙ and M h ≈ 7 × 1011 M ⊙, and the dwarf galaxy within its virial radius. Although the absorption is aligned with the extended major axis of the larger galaxy, the line-of-sight velocity of the absorbing gas is inconsistent with corotating accretion. The metallicity inferred for the LLS is lower than the gas phase [O/H] of the two galaxies. The mixture of cool and warm/hot gas phases for the absorbing gas and its proximity and orientation to the galaxy pair points to the LLS being a high-velocity gas in the combined halo environment of both galaxies.