Heaps rhymes with:
beeps, creeps, epes, jeep's, jeeps, keeps, leaps, peeps, reaps, seeps, sheep's, sheeps, sleeps, sweeps, weeps
Heaps sounds like:
habeas, habeck, habich, habig, habs, hafez, haffez, hafif's, hapag, hapke, hauppauge, havas, haves, havis, havoc, hbox, heaves, heavies, hibaaq, hibachi, hibbs, hippies, hippos, hipps, hips, hives, hoback, hobaugh, hobbes, hobbies, hobbs, hoboes, hobs, hoefs, hoffa's, hoofs, hoopes, hoops, hooves, hope's, hopes, hopke, hoppes, hopps, hops, hovious, hovis, hubbs, hubco, hubka, hubs, huebsch, huff's, huffs, huffy's, hypes, hypoxia