Max was born on Earth of an infamous lineage. A distant offspring of Khan Noonien Singh, one of the genetic "Superman" that ruled during the Eugenics Wars of the late 20th century.
Max carries the name and stigma associated with his ancestor and the secret society, "Chrysalis", that paired Singh's and other genetically altered offspring in an attempt to maintain the genetic superiority. The society was discovered and eliminated over 100 years ago, but Max still carries much of the genetic superiority of his ancestors.
Max joined the Starfleet Marines at age 17 and his superior genetic lineage allowed him to excel as a soldier and leader. Max earned the nickname "Mortis" for the high number of kills he obtained as a Marine.
Max fought in many actions and after a four year tour of duty Max ,was accepted into Starfleet Academy. Max graduated with honors from Starfleet Academy, but was always closely watched due to his heritage.
Following the Borg assault that decimated the command staff of his ship, Max assumed command and has been in command ever since.
A certain way to raise Max's ire is to questions his loyalty to Starfleet.
Max's brothers Montalbon and Xavier, along with his sister Anastasia are also Starfleet officers and their uncle Maximillian Khan Singh, is a Fleet Admiral in Starfleet.
Anastasia serves as Max's Tactical Officer and First Officer on the USS Botany Bay.
I haven't written up one for my joined Trill, aside from stating that he's the xth (don't remember the generation w/o looking it up) host of the Behl simbiont. Don't really know enough about the Trill to come up with a good bio, and I never watched DS9.
I try to keep mine short. I really hate when people have 3.5 pages of bio that I'm supposed to read when I look at their info. I get about half of a paragraph then they leave.