There are 119 substories in Yakuza 3 Remastered. Unlike most other Yakuza games, substories are not numbered, and several of them only reveal themselves after performing certain undocumented feats.
Here are some of the easiest substories to miss:
22 - Rough Draft. Score 1,100 on the Hard course at the Batting Center.
27 - The Hustler's Challenge. Win 3 games of nine-ball pool at Aqua Sky.
28 - Talking About Me? Visit the Love In Heart parlor at least once.
53 - Bullseye of Love. Play the 01 Darts game five times, then visit Bantam.
83 - Death Bowler. Score 200 in Bowling.
88 - Presidential Golfer. Get par or better in Competition Mode at the Golf course.
Also, be aware that there are some substories that are only triggered if you have Rikiya or Haruka with you, and there are other substories that can only begin if you are alone. There are also substories that only appear at night.
The final substory, "Amon", requires that you have completed all other 118 substories, all the Hitman missions, and all the Minimada training sequences. Plus, it must be night-time. The substory begins when you speak with Ibuki at the HLA.