Meet Todo
Must have a reputation of either equal or higher to getting Kobayashi unto your team, he is located at the 2nd shopping place in the game

Meet Titus
Must have a reputation of either equal or higher to getting Thor unto your team, he is located at the 2nd shopping place in the game

Have Ted join your posse
Decline Rex's offer to join and leave the area, come back to where Rex was, beat everyone up, and then you shall meet Ted

Have Jesse join your posse
Beat Turk 5 times and Jesse will appear (requires high reputation for him to join you)

Get Sonokwa and the Senridai Bombers
Play as 1 player without Riki and beat the Senridai Bombers anywhere 3 times then go to the 2nd place in the game and beat everyone there

Get Kumada
Decline Himada's offer to join you and come back and fight everyone and Kumada will be there

Fight Riki/Kunio
Start the game in 1 player mode only not 2 player mode and go outside the 2nd factory and you will fight your ally