I remembered the other day that Amadeus was nominated twice for the same category: both F. Murray Abraham and Tom Hulce were nominated for Best Actor. (Abraham won.)
Any other examples? Note: nominations for Best Actor and Best Supporting Actor don’t count, it has to be the same exact category.
The original Godfather had three actors nominated for Best Supporting Actor: James Caan, Robert Duvall, and Al Pacino.
Rocky had two supporting actor nominations: Burgess Meredith and Burt Young.
It happens often enough, especially in the Supporting Actor/Actress roles.
There have been a ton of double nominations, but only a handful of triples (* indicates eventual winner):
1935 Best Actor: Clark Gable, Charles Laughton, Franchot Tone–Mutiny on the Bounty
1954 Best Supporting Actor: Lee J. Cobb, Karl Malden, Rod Steiger–On the Waterfront
1972 Best Supporting Actor: James Caan, Robert Duvall, Al Pacino–The Godfather
1974 Best Supporting Actor: Robert DeNiro*, Michael V. Gazzo, Lee Strasberg–The Godfather, Part II
1963 Best Supporting Actress: Diane Cilento, Edith Evans, Joyce Redman –Tom Jones
Every one of these was a Best Picture winner (as was your example, Amadeus). Other double nods for Best Picture winners:
1939 Best Supporting Actress: Olivia de Havilland, Hattie McDaniel*–Gone with the Wind
1942 Best Supporting Actress: Dame May Whitty, Teresa Wright*–Mrs. Miniver
1944 Best Actor: Bing Crosby*, Barry Fitzgerald–Going My Way
1947 Best Supporting Actress: Celeste Holm*, Anne Revere–Gentleman’s Agreement
1953 Best Actor: Montgomery Clift, Burt Lancaster–From Here to Eternity
1969 Best Actor: Dustin Hoffman, Jon Voight–Midnight Cowboy
1976 Best Supporting Actor: Burgess Meredith, Burt Young–Rocky
1979 Best Supporting Actress: Jane Alexander, Meryl Streep*–Kramer vs. Kramer
1980 Best Supporting Actor: Timothy Hutton*, Judd Hirsch–Ordinary People
1983 Best Actress: Shirley MacLaine*, Debra Winger–Terms of Endearment
1983 Best Supporting Actor: John Lithgow, Jack Nicholson*–Terms of Endearment
1986 Best Supporting Actor: Tom Berenger, Willem Dafoe–Platoon
2002 Best Supporting Actress: Catherine Zeta-Jones*, Queeh Latifah–Chicago
But there have been a ton of other examples over the years, too.
One that comes to mind is Becket which had both Peter O’ Toole and Richard Burton nominated for Best Actor. Neither won since what can often happen in cases like this is that the two nominees will cancel each other out.
In 1994, three of the five songs up for Best Song were Elton John compositions from “The Lion King”:
"Circle of Life
“Hakuna Matata”
“Can You Feel the Love Tonight” (which won)
And in 1991, three of the five nominees were Alan Mencken songs from “Beauty and the Beast”
“Be Our Guest”
“Belle”
“Beauty and the Beast” (which won)
Just this year, two songs from “Slumdog Millionaire” were nominated; I would think this category has a LOT of multiple nominations.
“Enchanted” was also up for three songs, “Dreamgirls” for three, “Cold Mountain” for two, “The Little Mermaid” for two, “White Nights” for two, “Footloose” for two.
In 1983, two movies got two nods in the category; “Yentl” and “Flashdance.”
Some movies are song driven.
Doubt had two Supporting Actress nominations this year (Amy Adams, Viola Davis). Thelma and Louise also came to mind for Best Actress (Susan Sarandon and Geena Davis).
For Sleuth(1972 version) every single member of the cast was nominated for the Best Actor award.
Not in the Academy Awards, they weren’t. Eve Channing would have been a very strange nomination for Best Actor. 
Sheesh, I’ll have to watch Sleuth again. IMDB lists six cast members. (Five in reality). For the life of me, I only remember Olivier and Caine in it. I certainly don’t remember seeing the wife or the other two cops.
Any scenes with Eve Channing, if shot, ended up on the cutting room floor. The only thing you see of Margherite was her portrait in oils.
[spoiler] Of Course, in Sleuth there are only two roles, but it spouils things if the audience knows in advance that Inspector Doppler is Milo in disguise, or that Inspector Tarrant and the constable won’t show up. I suspect that they listed Eve Channing just to flesh out the cast list.
When Sleuth played on Broadway they did it up even classier – they came up with complete fake biographies for “Stanley Rushton” (who “played” Inspector Doppler) and the other actors, right down to fake credits for past plays. I suspect that people who really knew their theater could pick up on this, but if you don’t have fanatical devotion, you could miss the clues.
[/spoiler]
Have you checked her IMDB profile?
Actually, it’s just possible that you know this already and are whoosing us.