Sheer rhymes with:
bashir, cashier, chachere, schear, scheer, shear, shere, adhere, alvear, amir, appear, auctioneer, austere, bahir, bandolier, bashir, bassir, beare, bebear, beer, belvedere, bere, bioengineer, bombardier, briere, brigadeer, brigadier, budgeteer, career, casebeer, cashier, cavalier, chachere, chandelier, charpentier, cheer, chevalier, chusmir, clear, cleere, cohere, commandeer, conventioneer, crear, creer, crochetiere, cyr, davir, dear, deer, deere, desir, disappear, domineer, dornier, dubilier, dyneer, electioneer, emir, engineer, exovir, fear, fier, financier, financiere, fleer, frear, freire, frontier, gear, geer, gere, gier, giere, gondolier, grear, greer, guinier, imagineer, insincere, interfere, jeer, kamir, kear, kier, kir, kleer, kneer, lagardere, laimbeer, lanier, lazear, lear, marketeer, mateer, mclear, mcnear, mcneer, mcteer, mear, meir, menear, mere, minear, minteer, mir, mutineer, myhre, near, neer, nir, o'lear, olear, oneyear, orear, pamphleteer, peer, pelletier, persevere, pier, pioneer, plenmeer, premier, premiere, profiteer, puryear, queer, racketeer, rainier, rayonier, reappear, rear, reengineer, rensselaer, revere, rosevear, safier, sameer, samir, schear, scheer, schweer, sear, sere, severe, shamir, shear, shere, sincere, smear, sneer, souvenir, spear, speer, speir, sphere, stear, steer, steere, st_cyr, summiteer, teer, termeer, unclear, vanleer, vanliere, veer, veneer, vere, volunteer, wagoneer, wazir, wier, year, zahir, zaire, zamfir, zegeer, zerr, zier
Sheer sounds like:
saar, saari, sacher, sacra, saeger, sagar, sager, saguaro, sahara, sahr, saker, sakura, sakurai, sar, sara, sarah, sare, sari, sarowiwa, sarra, sarro, sasser, saucer, saucier, sauer, saur, saurer, sauro, sauser, sausser, sawyer, saxer, sayer, sayre, scar, scare, scarier, scarry, scary, schaar, schacher, schaecher, schaer, schairer, schar, schara, scharer, scharr, scharrer, schauer, schear, scheer, scheerer, schehr, scheier, scheirer, scher, scherer, scherr, scherrer, scheuer, scheurer, schicker, schier, schiesser, schiro, schor, schorr, schreier, schreur, schreyer, schrier, schroer, schroyer, schryer, schucker, schur, schurr, schuur, schwager, schwaiger, schweer, schweiger, schweizer, schwer, schwieger, schwier, schwoerer, sciara, sciarra, scire, scissor, scohier, scor, score, scorer, scour, screw, screwy, scurry, seager, sear, seashore, secor, secure, seeger, seeker, seer, seery, segar, segarra, seger, segur, segura, seher, sehr, seier, seiger, seiser, seizure, sequeira, sera, seraw, sere, seria, serio, serr, serra, serrao, seskar, sewer, sexauer, sexier, seyer, sgro, sgroi, shaer, shahar, shaker, shakier, shakir, shakur, shara, sharaa, sharar, share, sharer, shareware, shari, sharia, sharrar, sharrer, sharrow, sharry, shauger, shear, shearer, sheerer, sher, shere, sheree, sherer, sheri, sherr, sherrer, sherri, sherrie, sherrow, sherry, shier, shigeru, shir, shira, shirah, shire, shirer, shirey, shirr, shocker, shoichiro, shor, shore, shorey, shorr, shower, shri, shroyer, shugrue, shukri, shur, shure, shurr, sicker, sieger, sierra, sigur, sikora, sir, sire, siri, sirohi, sirri, sixer, sizer, skaar, skare, skerry, skewer, skier, skora, skura, soaker, soar, soccer, sochor, soir, soiree, sor, sore, sorey, soria, sorrow, sorry, souccar, sour, sower, square, squeaker, squier, squire, sr, sri, successor, succor, sucher, sucker, suckrow, sucre, sueker, sugar, sugary, sugihara, sugrue, suhr, suhre, suire, sukru, sur, sura, sure, surer, surrey, surry, susser, swager, swagger, swauger, swear, swecker, sweger, swier, swiger, swire, swisher, swissair, swogger, swor, swore, swoyer, sycara, sykora, syria