Moore, 46, who has three daughters with her ex-husband Bruce Willis, wed the funnyman in 2005 and recently admitted she would love to have a child with her younger partner.
The star's eldest daughter, Rumer Willis, revels in her new family set-up - and is hopeful her mum will cement her brood by falling pregnant for a fourth time.
She says, ''I love the idea. After all, our family continues to grow in so many ways all the time - growing in numbers could be a good thing."
And the 21 year old is hoping a future sibling will be a boy - so she and her two younger sisters, Tallulah and Scout, can ''show him who's boss".
The 21 year old followed in the footsteps of her Hollywood superstar parents Bruce Willis and Demi Moore by launching a career as an actress, and recently starred in her first major Hollywood film as a lead in Sorority Row.
But Willis is adamant she won't get sucked into the fame game - because she'd rather cook up a storm in the kitchen.
She tells Britain's Glamour magazine, "I just don't care about fame. I have better things to do like making pies.
"I love making pies. It all started when I went on a road trip with my boyfriend. We stopped off at this diner and had this strawberry and rhubarb pie, and I thought, 'This is incredible. I'm going to learn how to make it'. So I did."
And it seems her cooking is a hit with the A-listers - her mum Moore and stepdad Ashton Kutcher are huge fans of her baked goods.
Willis adds, "My mom likes either pecan pie or German chocolate and I just made a coconut banana cream pie for Ashton. He liked that very much. It was gone in a matter of three days."
Rumer Willis has yet to bare all on the big screen, but she insists it's not a clause in her contract and she would go naked if it was necessary.
She says, "If it's nudity just because they want you to get naked in a movie, then I'm kind of like, 'You know what? No.' But if it's kind of pivotal, and it helps move the story along, then yeah, sure I'll do it."
But she won't be inviting her Die Hard dad to that premiere, adding, "I can't imagine being like, 'Hey Dad, wanna come?' I'll just have to wait for it to come out on DVD, so I can fast forward through those scenes."
"I would never want the responsibility of being the prettiest girl onscreen. Growing up with a mother like mine gives you a skewed idea of what a mother should look like. My mother's jeans are smaller than mine!" RUMER WILLIS is aware of mum DEMI MOORE's striking good looks.
The 21 year old has embarked on her own Hollywood career appearing in a string of movies, including upcoming horror remake Sorority Row, and filming a role in teen TV show 90210.
She appeared alongside her actress mum in 1996 film Striptease, and with her dad in The Whole Nine Yards in 2000 and in 2005's Hostage.
But Willis now wants to star with her parents in a more challenging role.
She says, "Sometimes I think we helped each other by playing opposite each other. When my dad has to do a super-emotional scene, he looks at a picture of us to find the emotion. Playing his kidnapped daughter in Hostage meant he didn't have to look at the picture to get kind of tearful.
"I'd love to work with my parents again, now that I'm older. I'd love to play someone other than their daughter."
"I sent my mum and my dad a picture and they were like, 'Wait, you're not really (pregnant)!' I said, 'No, no,no, I'm doing it for a show guys, don't worry.' They were like, 'You scared me for a second.'" RUMER WILLIS freaked her mum DEMI MOORE and dad BRUCE WILLIS out when she sent them pictures of what she'd look like pregnant. The actress plays an expectant teen in U.S. TV series THE SECRET LIFE OF THE AMERICAN TEENAGER.
Kutcher was in town with his wife, Demi Moore, to celebrate his step-daughter, Rumer Willis' 21st birthday over the weekend (15-16Aug09).
And the star made the most of his time in the gambling Mecca by teaming up with German artist NOMAD on Sunday (16Aug09) to "tag" the roof of the Planet Hollywood Resort and Casino.
The pair painted a large white outline of a slot machine with the words "Lucky Me".
But the devilish duo didn't get into trouble over the stunt - they asked the hotel's owners for permission first, according to People.com.
Kutcher boasted of his achievement in a post on his Twitter.com, telling fans, "Just tagged the roof of Planet Hollywood.".
“I had always wanted a dog and my dad came home one day and he had something wrapped up in a towel. He was just holding it and we were talking in the kitchen for a good 10 minutes or so and he just said, ‘Oh here, can you hold this for me?’ And it was a puppy.” RUMER WILLIS recalls her favourite childhood birthday present from her famous dad BRUCE.
The young actress, whose parents split when she was just 12, toasted the landmark age at celebrity hangout Tao at the Venetian Hotel in the gambling Mecca.
Willis was joined by her whole family, including her famous father and his new wife Emma Heming, mother Moore and her husband Ashton Kutcher, her younger sisters Tallulah and Scout, as well as her boyfriend, Micah Alberti, The Hills star Audrina Patridge and other cast members of her upcoming movie, Sorority Row.
Willis was handed two birthday cakes and the guests were treated to a performance from a troupe of Sin City showgirls, an Elvis look-a-like and a Madonna impersonator.