Here's what rhymes with branchiomerism.
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rhythm arisen risen mizzen given vision listen mission prison fission riven addition driven edition ambition emission incision omission derision magician envision imprison audition stiffen glisten position condition decision division commission permission physician admission algorithm petition coalition collision intuition nutrition revision excision forgiven ignition musician remission tuition apparition attrition erudition fruition sedition technician volition dentition logarithm rendition striven logician rhetorician munition prevision rescission definition opposition tradition provision television transition precision repetition suspicion abolition ammunition cognition deposition exhibition inhibition partition prohibition submission clinician imposition admonition demolition transposition apposition contrition indecision intermission paroxysm patrician cataclysm manumission theoretician dietitian ebullition readmission tactician competition composition recognition transmission acquisition disposition expedition supervision exposition politician supposition circumcision mathematician requisition inquisition precondition electrician premonition academician imprecision proposition decomposition superstition subdivision malnutrition preposition extradition interposition redefinition disquisition obstetrician pediatrician predisposition indisposition presupposition superposition statistician diagnostician juxtaposition superimposition wisdom serum theorem cecum gingham system kingdom victim dictum gypsum fearsome winsome symptom pilgrim ecosystem