In Ghostbusters II, Dana Barrett (Sigourney Weaver) has a baby son. His name is Oscar, but we never find out his last name and it strongly implied that his father is not Peter Venkman (Bill Murray), but actually that of the violinist from the first film. You know, the one Venkman refers to as the "stiff" and Dana refers to as "nose spray." In the clip below, Dana briefly mentions that Oscar's father left them to go play for the London symphony. Perhaps, Dana was lying and it is actually Peter's love child. I'm sure we'll find out in Ghostbusters III as Oscar is locked in to play a major role in the film as a fellow Ghostbuster.
Sigourney Weaver says that during one relatively recent conversation with Ivan Reitman, “I said, I have one condition want my son Oscar [from Ghostbusters II] to be a Ghostbuster, and he said, ‘We’ve already done that.’”
Also, Phil Lord and Chris Miller, the pair that have directed 21 Jump Street, The Lego Movie, and 22 Jump Street, explained to ScreenCrush why they passed on the opportunity to direct Ghostbusters 3.
Right now, we’re just super tired and we want to take a break. We’re doing a TV show with Will Forte. So, we don’t really know what we’re gonna do next, we just know we can’t jump into another movie like that right away.
GHOSTBUSTERS II - After waging a war on slime that cost New York City millions, the Ghostbusters find themselves out of business until an ancient tyrant, preparing a return to the Earthly domain through his portrait at the Manhattan Museum of Art, sets his sights on Dana Barrett's baby as the new home for his wicked soul! With the help of the Museum's possessed curator, he plans to turn New York into a really scary place to live! Now only the Ghostbusters can save New York City, by turning paranormal pest control into an art form!
Cast: Bill Murray, Dan Aykroyd, Sigourney Weaver, Harold Ramis, Rick Moranis, Ernie Hudson,
Annie Potts, Peter MacNicol, Harris Yulin, David Margulies, Kurt Fuller
Director: Ivan Reitman * Screenwriters: Harold Ramis & Dan Aykroyd