John Maxwell was one of at least seven children born to Bazil/Bazel Maxwell.

His known siblings were Mary, Fanny, Elizabeth, Ann, William K., and Margaret Jane. There may have been a son, Thomas, born c1822 (between Elizabeth (1820) and William (c1825) who died before Bazel's death in 1837 as he is not listed in the guardianship paperwork of 13 Nov 1837.

On 8 Mar 1834, John married Mahala Weddle in Salt Creek Twp., Jackson County, Indiana. They had nine children: Elizabeth Ellen, James Jefferson, Enoch William, David H., Edward Bazeleel, Annis Louise America, Mary Jane, Nancy Adeline, and John W.
~~~~~~
According to Daniel Maxwell (a 3rd great-grandson), John's middle name is "Chester", while all the documentation that I've seen lists "P." as a middle initial. If anyone has documentation, please contact me.
Update - 12/7/12:
I know I am the one who had you add 'Chester' as John's middle name, but after a bit of digging I cannot prove this. There is only one small piece of evidence that his middle initial was 'C' but I dont have the original record, just a transcript. There is also however no proof that I have found that he had a 'T' middle initial either, and I maintain that those that have him as John T Maxwell are confusing him with John T Maxwell, son of John Maxwell and Rebecca Anderson.
Here is the single reference I have to him having a 'C' middle initial:
From the Seymour IN Daily Democrat Oct 21 1886:
"John C. Maxwell of Freistatt, MO., is here visiting his daughter, Annis Luiza whom he has not seen for over 17 years."
If I can get ahold of this newspaper and it doesnt have a C after all, I will say there is no proof John had a middle name, but until then I would probably removed the 'Chester' or remove the middle initial completely.
~~~~~~
2/13/12: "I remember when" (FindaGrave contributor #47097113)

John Maxwell married a second time when his first wife died. He married Elizabeth Ellen (Brewer) Young. Her 1st husband, Isaac had passed away. They were married on January 23, 1887 in Barry county, Missouri. When John died in 1901 he was buried next to his first wife. Elizabeth is buried in Avilla Cemetery. Elizabeth 'Eliza' received her husband John's Civil War pension.
~~~~~~~~~~~~~~~~~
Thank you, Vickee Rae for sending the following:
12 Sept 1901 Cassville Republican
Died: At Mineral Springs, Tuesday, Grandpa Maxwell or 'Uncle John', as he was commonly called.
He was an old and well respected citizen of this county and never moved but what the neighbors felt they had lost a good neighbor. He leaves a wife and six children, three sons and three daughters.
His oldest son, Dr. Maxwell, lives near Cape Fair, Edward near McDowell, John, west of Exeter, Mrs. Hillhouse in Lawrence County, Mrs. Wynkoop in Cassville, Mrs. McKinney near Cassville.
Grandpa Maxwell did not live in vain. He did his duty as a citizen and father. He was a member of the M P Church; was buried at Mineral Spring after religious services conducted by the writer. He was over 88 years old.
Rev J W Ennes