May 18, 2018 05:55 PM

The more the merrier for Alec and Hilaria Baldwin.

The couple welcomed their fourth child and third son together on Thursday, they both announced on Instagram, sharing a sweet photo of themselves in the hospital with their newborn baby boy.

Hilaria, 34, captioned her snapshot, “He’s here! He’s perfect! 8lbs 2oz 💛 #wegotthis2018,” explaining in a follow-up post Friday that the couple are “still choosing his name.”

Already mom to Leonardo Ángel Charles, 20 months, Rafael Thomas, 2½, and Carmen Gabriela, 4½, Hilaria shared with PEOPLE following her pregnancy announcement that she wasn’t sure she and Alec, 60, are done expanding their family.

“I never knew how many kids I wanted to have,” she said in November, shortly after revealing baby No. 4 would be a boy. “I didn’t know how much I’d like [motherhood]. And I really, really like it.”

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RELATED: Hilaria Baldwin Steps Out One Last Time in Bump-Hugging Dress Before Baby No 4 Arrives

With three kids under four at the time, the busy parents initially thought their family was complete. But after welcoming Leo, Hilaria says she and Alec began thinking about another baby and ultimately decided to take a different approach to getting pregnant.

“We were like, ‘Oh, should we have another kid?’ ” she told PEOPLE. “We were like, ‘You know what? Let’s try something different — let’s try.’ [With] the other ones, it’s not like we were like, ‘Oh my God, how did this happen?’ But this is the only one we [planned].”

Hilaria and Alec Baldwin
Desiree Navarro/WireImage

RELATED VIDEO: Alec and Hilaria Baldwin Welcome a Son

One reason the couple may consider another baby is that Carmen, with two little brothers already, really had her heart set on another girl joining the family. (Alec is also dad to daughter Ireland, 22.)

“She was a little bit disappointed. [She said,] ‘How about you have a girl first, then you can have another boy?’ I was like, ‘It doesn’t work that way! I don’t get to choose,’ ” the yoga instructor recalled.

“She’s like, ‘No, you don’t understand, Mommy. It’s going to be a girl.’ I was like, ‘No, I promise. I promise you it’s a boy,’ ” Hilaria added. “She is committed to a fifth child.”

She continued, “I’ve had so many [kids] because I really like them and we have such fun times. I’m going to have four kids in a little over four years and it’s just one of those things where I’m going to let life lead me in that direction.”

RELATED: Pregnant Hilaria Baldwin Is Excited for Baby No. 4 But Admits She Might “Have Another Meltdown”

Alec may have his work cut out for him with another child, though. In March, the Match Game host appeared on The Tonight Show, where spoke to Jimmy Fallon about the couple’s rapidly expanding household.

“We’re having children — it’s outpacing our ability to house them,” he joked. “I said to my wife, ‘This one, we’re going to have to put him in a hotel. He’ll be nearby.’ “

“My daughter Carmen said, ‘You have to have another one. We have to have another girl so we have another girl in the house. And my wife says to me, ‘I want to have maybe one more, Alec. We have one girl,’ ” the comedian explained, adding jokingly, “And I said, ‘I hope you and your next husband are very happy together.’ “

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