Here's what rhymes with engagei.
                        
                        
                    
                                day  pay  j  bay  che  dey  jay  payee  rj  tae  bey  they  may  way  say  play  re  lay  stay  array  gay  k  obey  pray  ray  hay  nay  prey  weigh  tray  fay  fe  oj  yea  hey  ij  ley  rei  sei  whey  bj  bk  drei  fj  kc  lei  rea  tj  tre  wei  bray  dray  neigh  brae  cay  fey  roue  shay  trey  spay  copay  away  today  delay  clay  decay  essay  gray  grey  okay  spray  ballet  cafe  repay  stray  sway  fray  slay  allay  bouquet  ok  passe  sleigh  cabaret  saute  zwei  flay  belay  splay  moray  purvey  toupee  aurae  aweigh  survey  anyway  convey  everyday  betray  dismay  astray  valet  attache  cliche  defray  disarray  fillet  dossier  emigre  gangway  naturae  puree  replay  crochet  croquet  getaway  parquet  workaday  filet  inveigh  airplay  byplay  nisei  prepay  sachet  sorbet  hooray  noway  overpay  sickbay  briquet  caesurae  hurray  layaway  outplay  outstay  reweigh  umbrae  underpay  misplay  display  yesterday  holiday  halfway  interplay  portray  underway  disobey  naivete  overlay  papillae  waterway  matinee  microarray  toothache  underlay  alleyway  maxillae  risque  soiree  souffle  wordplay  caraway  carriageway  castaway  giveaway  hideaway  ricochet  patellae  pleurae  soubriquet  stowaway  underplay  macrame  overplay  overstay  urethrae  medullae  bobsleigh  copulae  penumbrae  tearaway  respray  runaway  vertebrae  faraway  lamellae  passageway  protege  sequelae  francais  nebulae  societe  breakaway  fistulae  lingerie  scapulae  sobriquet  straightaway  cabriolet  fibulae  throwaway  resurvey  stingray  takeaway  flyaway  roundelay  foldaway  walkaway  formulae  uvulae  cybercafe  communique  trabeculae  salmonellae  tarantulae  companionway  caravanserais