Not necessarily for that picture.
I can think of two pictures in which the actors appearing during their careers won a total of 8 Oscars
Bad Day at Black Rock won no acting Oscars. Spencer Tracy had two Best Actor Oscars. Walter Brennan had 3 Best Supporting Actor Oscars. Dean Jagger had one Best Supporting, Lee Marvin and Ernest Borgnine each had one Best Actor award.
Philadelphia saw Tom Hanks win one of his two Best Actor awards. Denzel Washington has one each for Best Actor and Best Supporting Actor. Joanne Woodward has one Best Actress. Jason Robards has two Best Supporting Actor Awards. Mary Steenburgen has a Best Supporting Actress.
Close behind is Guess Who’s Coming to Dinner with 7 awards. The aforementioned Spencer Tracy still has two, and Katherine Hepburn won one of her four Best Actress awards for her role. in his picture (winning her third one year later for A Lion in Winter). And of course Sidney Poitier has a Best Actor award.
Also close behind is the film with the fourth and final Best Actress for Heburn, On Golden Pond, which also had Jane Fonda who won two Best Actress Oscars and her father Henry Fonda winning his Best Actor Oscar, giving us another film with a total of 7.
I am doing this from memory, as a long-time film buff.
Off the top of my head these are the leaders, but I am sure others here can add films with actors in them with multiple Oscars, perhaps more, perhaps equaling these four films.
Yes I know Lincoln had 6 s- far — 3 Best Actor for Daniel Day-Lewis (who won for this film), two Best Actress for Sally Fields, and one Best Supporting Actor for Tommy Lee Jones, but I did not want to go lower than 7.
Feel free to add in the comments any films with the performers with more than 8, or with 8 or 7.