- Son of Academy Award-winning director Anthony Minghella and choreographer Carolyn Choa.
- Graduated from Columbia University in 2009.
- Was in a relationship with Kate Mara from 2010 to 2014.
- Childhood crush was Kirstie Alley in Look Who's Talking (1989).
- Max's ancestry is approximately one half Italian, 9/32 Chinese (equivalent to 1.125/4 Chinese), 1/16 Indian Jewish, 1/16 Parsee Indian, 1/32 English, 1/32 Irish, and 1/32 Swedish.
Max's paternal grandfather, Edward Minghella, was an Italian immigrant, and Max's paternal grandmother, Gloria Alberta Arcari, was born in Leeds North, England, to Italian parents.
Max's maternal grandfather, George Wing Sien Choa, was born in Hong Kong, of three quarters Chinese, and one quarter Indian Jewish, ancestry. George was a prominent otorhinolaryngologist (in simple English, an ear, nose and throat doctor - an ENT). George's maternal grandfather, Max's great-great-grandfather Emanuel Raphael Belilios, who was born in Calcutta, was a prominent businessman.
Max's maternal grandmother, Maisie Nora Kotewall, was also born in Hong Kong. Maisie's father, Robert Hormus Kotewall, was a well-known Hong Kong businessman and legislator; Robert was of approximately half Parsee Indian and half Chinese ancestry. Maisie's mother, Edith Lowcock, was of approximately one quarter English, one quarter Irish, one quarter Swedish, and one quarter Chinese (through Max's matrilineal line), ancestry. - Former member of the National Youth Theatre.
- Half-brother of Hannah Minghella.
- Nephew of Edana Minghella and Dominic Minghella.
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