How sure are you they lived in MI to 1920?
There is a tree I found which has a Joseph Cassatay born March 21, 1864 (does not say where)
died Sept. 14, 1911 Chicago, IL
father Dominick (no age or other info given for him)
Joseph married to Sarah White born Jan. 1, 1877 Chicago, IL
died June 17, 1929 Chicago, IL
they show one son Walter J. Cassidy born Aug. 16, 1897 Chicago, Il
died 1969 Chicago, IL
wife Jean Ann Maroney 1908-1907
do the names Sarah White and Walter match with anything you have.
You said Joseph was your grandfather so you must know the name of at least one of his children.
I then went to records and found Joseph Cassidy with same birth and death dates shown in the tree - Cook County, IL deaths show though that Joseph was born Michigan, father is Dominick Cassidy born Germany
mother born Germany - no name given
Here is the 1900 census for the family - some info does not agree with the tree, but then census info is often wrong or ??
1900 CHICAGO WARD 34, COOK, IL
Jos., age 34, teamster, born March 1866,IL parents born IL married 7 years
Sarah, age 31, wife, born June 1868IL parents born IL married 7 years, 2 children born 2 living
Elmer, age 5, son born Feb. 1895,IL parents born IL
Walter, age 3,son born Aug. 1896IL parents born IL
1910CHICAGO WARD 33, COOK. IL
Joseph, age 48, teamster, milk dairy, born Aust. Switzerland parents born Aust. Switzerland, immigrated 1866, 1st marriage, married 17 years
Sarah, age 40,wife, born IL parents born Ireland, 1st marriage, married 17 years, 7 children born 5 living
Elmer, age 15, son
Walter, age 12, son
Gertrude, age 8, daughter
Evelyn, age 4, daughter
Elsie, age 4/12,daughter
all children born IL father born Aust.Switzerland, mother born IL
So census and death records for Joseph show different places of birth, MI. IL, and Aust. Switzerland
1920 CHICAGO WARD 9, COOK, IL
Sarah, age 48, widow, born IL parents born Ireland
Walter, age 22, son, switchman, railroad, born IL
Gertrude, age 18, daughter, clerical, insurance, born IL
Evelyn, age 14, daughter, born IL
Francis, age 10,daughter, born IL
all children show father born MI mother born IL
so once again Joseph's birthplace shown as MI
So from all of this, are there any names you recognize? Since Joseph is your Grandfather , one of his children is either your father or mother so are they listed in any of those records?
I'm going to look a bit more and will post if I find anything else.