Monochrome Factor, Sougiya Riddle Recommendations
Both stories are about a high school boy as the main character who meets a suspicious, long-haired, hat-and-trench-coat-wearing man. Said man demands help with dealing with fighting supernatural opponents.
Premises are practically identical: a man from the spiritual realm (having long hair, dressed in black clothes and a hat) apprentices a high school boy after said boy loses part of his soul. The boy assists the man in his work fighting evil spirits (and powers up into a cool outfit).
Monochrome is more shounen, Undertaker is more shoujo.
in both a boy meets a strange man, and they both team up and fight in random battles , often starting out with the young boy unwilling at first then becomes more used to it over time.