Rummaging rhymes with:
damaging, imaging, acknowledging, averaging, damaging, disparaging, encouraging, foraging, hemorrhaging, imaging, leveraging, messaging, micromanaging, mismanaging, mortgaging, packaging, pillaging, presaging, ravaging, repackaging, salvaging, savaging
Rummaging sounds like:
ranching, ranging, rangoon's, ranking, rankings, rankins, ransacking, ransom's, ransoms, rearranging, reinking, remaking, reminiscence, reminiscences, reminiscing, remissions, renaissance, renaissance's, reneging, renouncing, rensing, ringing, ringneck, rinsing, romancing