• agony aunt

• crack of dawn
• all gone
• far gone
• and so on
• bank on
• bargain on
• be hard on
• be on
• blow the whistle on
• border on
• bring on
• brush up on
• carry on
• cash in on
• cast doubt on
• catch on
• check up on
• cheer on
• come down hard on
• come on
• count on
• cut one's eyeteeth on
• cut one's teeth on
• cut your teeth on
• dash cold water on
• dawn on
• death on
• develop a crush on
• die with one's boots on
• do a job on
• down on
• draw a bead on
• draw on
• edge on
• egg on
• fasten on
• feast one's eyes on
• figure on
• get a fix on
• get a grip on
• get a head start on
• get a line on
• get a wiggle on
• get in on
• get on
• get one's hands on
• get the lowdown on
• get the upper hand on
• go back on
• go on
• going on
• hand on
• hang on
• hang one on
• hard on
• have an edge on
• have on
• have one's ears on
• have one's eye on
• have something on
• have the goods on
• have the jump on
• have the laugh on
• head on
• high on
• hold on
• home in on
• hooked on
• impose on
• in on
• jar on
• keep a close check on
• keep on
• keep one's eye on
• keep one's shirt on
• keep tabs on
• keep your hair on
• know which side one's bread is buttered on
• land on
• later on
• lay a finger on
• lay hands on
• lay on
• lay one's finger on
• lead on
• lean on
• leave without a leg to stand on
• leg to stand on
• let on
• let one in on
• look in on
• move in on
• movin' on
• moving on
• muscle in on
• not a leg to stand on
• not have anything on
• odds on
• one eye on
• pass on
• pick on
• pin one's faith on
• plan on
• play tricks on
• pour cold water on
• prevail on
• pride oneself on
• pull the other one, it's got brass bells on
• pull the plug on
• push on
• put a new face on
• put dibs on
• put on
• put one's hand on
• put someone on
• put the bite on
• rain on
• rat on
• rat out on
• read up on
• ride herd on
• right on
• rub off on
• run out on
• seize on
• sell one on
• set eyes on
• set one's heart on
• set one's mind on
• set your sights on
• settle on
• shed light on
• sign on
• sit in on
• sit on
• sleep on
• sneak up on
• sold on
• spot on
• steal a march on
• steal up on
• step out on
• stuck on
• sweet on
• switched on
• tack on
• take it out on
• take on
• take out on
• tell on
• throw light on
• to lean on
• trade on
• try on
• turn on
• turn one's back on
• wear on
• wish off on
• with bells on
• with one's boots on
• zero in on
• big yawn

One-syllable words do not have mosaic rhymes.