Here is the list of Tony nominated shows, by production:
Fela! – 11
La Cage aux Folles – 11
Fences – 10
Memphis – 8
Ragtime – 7
Red – 7
A View from the Bridge – 6
The Royal Family – 5
Enron – 4
A Little Night Music – 4
Promises, Promises – 4
American Idiot – 3
Finian’s Rainbow – 3
In the Next Room or the Vibrator Play – 3
Lend Me a Tenor – 3
Million Dollar Quartet – 3
The Addams Family – 2
Come Fly Away – 2
Everyday Rapture – 2
Hamlet – 2
Next Fall – 2
Sondheim on Sondheim – 2
Time Stands Still – 2
A Behanding in Spokane – 1
Collected Stories – 1
Looped – 1
Present Laughter – 1
Race – 1
Superior Donuts – 1