For the parallel plot be richer you could enhance your narrative working with a character that follows Mitch Albom's timeline from the beginner of the story till the end, you could work with the character of Morrie's brother, David.
To decide how you want David's character to be think about the environment he can bring in.
You could describe David as the opposite of Mitch Albom, as a caring and simple man, not so related to his accomplishments or with work as Mitch later became. Also you could give David a big family with children and set the story around David being widowed and busy caring for his family and trying to keep up regular meetings with Morrie, while Mitch was not around because was busy with his life. Then you might cross David path in the story with only Morrie or with Mitch as well, as Mitch visits Morrie in his house later on the story.