Afair you can meet a custom character ingame randomly & can increase the chance by visiting the places she likes, which is based on her personality. For this you have to add her to a town first via create a girl.
Because the above is rather laborious you have the option to pick a custom character up at the station & add her to the contact list. The station also offers to add new characters to the current town.
And there is more:
The "Discriminating Eye" Upgrade
"You have developed a keen eye for potential. Once per week, you can seek out a specific personality type at the train station."