The Wide Field Camera 3 (WFC3) on the Hubble Space Telescope (HST) enabled the search for the first galaxies observed at z∼8-11 (500-700 Myr after the Big Bang). To continue quantifying the number density of the most luminous galaxies (M AB ∼ −22.0) at the earliest epoch observable with HST, we search for z∼10 galaxies (F125W-dropouts) in archival data from the Brightest of Reionizing Galaxies (BoRG[z8]) survey, originally designed for detection of z∼8 galaxies (F098M-dropouts). By focusing on the deepest 293 arcmin 2 of the data along 62 independent lines of sight, we identify six z∼10 candidates satisfying the color selection criteria, detected at S/N>8 in F160W with M AB =−22.8 to −21.1 if at z=10. Three of the six sources, including the two brightest, are in a single WFC3 pointing (∼4 arcmin 2 ), suggestive of significant clustering, which is expected from bright galaxies at z∼10. However, the two brightest galaxies are too extended to be likely at z∼10, and one additional source is unresolved and possibly a brown dwarf. The remaining three candidates have m AB ∼26, and given the area and completeness of our search, our best estimate is a number density of sources that is marginally higher but consistent at 2σ with searches in legacy fields. Our study highlights that z∼10 searches can yield a small number of candidates, making tailored follow-ups of HST pure-parallel observations viable and effective.