bookkeeping
buccanneer
Those are consecutive letters in the English alphabet, starting with the letter 'k' and ending with the letter 'n'.
therein
therein
bookkeeper, bookkeeping
Successfully is a 12 letter word with three set of double letters. Stubbornness is another 12 letter word.
balloon
bladders
Savvy, letter, vacuum, and bubble have doubled letters.
addassallillofferrbeeseefeepeeteeweezooboocoogoomootoooddebb
buffcuffmuffpuffballbellbillbullcallcellmallmillmullnullpillpullrollsillselltilltelltallwallwellwillbassbosscussfusshisskisslessmessmissmassmosslosspasssasstossmuttmittbuttdollfallfellfillfull
This is every ten-letter word with three sets of double letters from two comprehensive dictionaries. I don't see any that are consecutive: accessless addressees annulettee arrowwoods barrenness bitterroot bookkeeper butterroot coffeeroom coffeeweed coffeewood committees commonness crookkneed fallenness hiddenness keennesses pepperroot rottenness schoolless sleepproof soddenness suddenness sullenness tallowweed tallowwood vassalless willowweed woodenness woolliness yellowweed yellowwood