Here's what rhymes with maximising.
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missing living giving fishing wishing kissing forgiving hissing sniffing sieving sufficing nonliving swishing dismissing thanksgiving misgiving unforgiving griffin reliving reminiscing knitting milling nearing nipping sitting willing appearing filling fitting killing singing winning mixing permitting picking shipping unwilling admitting bidding committing digging fearing forbidding hitting rearing ringing billing cheering chilling dipping emitting kicking omitting pitching rigging shearing shilling submitting thinning whipping gearing kidding licking milking pinning pitting ripping sinning sipping ticking tipping chipping ridding searing smearing sneering tiling tilling unwitting wringing chiming dimming ginning hitching leering mincing minting veering winging building thinking bringing clearing fixing lifting linking listing shifting sinking spinning swimming switching assisting clinging drilling piercing pioneering slipping splitting springing steering sticking swinging adhering bridging clicking clipping dripping grinning quitting sibling stripping thrilling whistling enriching filming flinging flitting gripping hinting lynching pinching positing risking sifting skimming skipping spilling spitting stinging stitching tilting trimming tripping twitching unthinking brimming fiddling flicking flipping gilding limping pricking remitting rinsing stringing tickling twinning winking abridging affixing consigning grilling lilting lisping pickling silting skidding skinning slinging slitting spearing whittling wilting wincing beginning consisting drinking engineering printing convincing disappearing drifting fulfilling insisting twisting persisting shrinking befitting blinking domineering enlisting equipping kindling persevering stinking subsisting trickling underpinning unremitting volunteering afflicting bewitching cringing electioneering fringing impinging instilling quilting scripting squinting unflinching clinking convicting evincing flinching glinting reappearing refilling refitting splinting sprinting stripling unblinking existing conflicting depicting interfering resisting transmitting inflicting rebuilding sprinkling distilling rethinking unconvincing counterfeiting imprinting infringing profiteering eclipsing predicting restricting coexisting constricting reprinting contradicting preexisting