Put bones in an 8-qt. pot and add just enough cold water to cover. Bring to a boil. Drain bones in a colander, discarding cooking liquid, and rinse well with cold water.
Return bones to pot with 5 qts. fresh, cold water. Add ginger, goji berries, and jujubes. Bring to a boil, partly covered; then reduce heat and simmer, covered, 4 to 6 hours, adding onions for last hour. Strain broth, discarding solids, and chill overnight. Skim off fat before using.
*Find at East Asian markets or online.