[1] As of 2014, McAllister has been Professor of Saxophone at the University of Michigan School of Music, Theatre & Dance,[2] a role held previously by Donald Sinta and Larry Teal.

He has premiered over 250 new works by composers including: Gunther Schuller, Caleb Burhans, Jennifer Higdon, Benjamin Broening, Kati Agocs, Mischa Zupko, Gregory Wanamaker, Roshanne Etezady, Kristin Kuster, William Bolcom, Martin Bresnick, Steven Mackey, Lee Hyla, Libby Larsen, Lei Liang, John Harbison, David Rakowski, Zhou Long, Chen Yi, Joel Puckett, Brian Fennelly, Evan Chambers, Ken Ueno, Donnacha Dennehy, David T.

[3] His recording of William Bolcom’s Concert Suite for Alto Saxophone and Band was nominated for multiple Grammy Awards.

This concerto was a joint commission by St Louis, Baltimore and Sydney Symphony Orchestras and Fundacao Orquestra Sinfonica do estado de Sao Paulo.

He is featured as the saxophone soloist on ‘City Noir’ (album) which won the 2014 Grammy Award for Best Orchestral Performance.