The X owner and singer share 4-year-old son X Æ A-12, 3 ½-year-old daughter Exa Dark Sideræl and son Techno Mechanicus, who was born in 2022

Elon Musk and Grimes hope to live with all of his children and their mothers.

A source tells PEOPLE that the X (formerly Twitter) owner, 53, and the singer, 36, recently went house hunting in Bel Air, searching for a home they can share with their three children as well as Musk’s other children and their mothers.

Musk and Grimes share 4-year-old son X Æ A-12, 3 ½-year-old daughter Exa Dark Sideræl and son Techno Mechanicus, who was born in 2022.

The insider tells PEOPLE that Grimes was also shown a home in Upper Bel Air. She and Musk are no longer romantically involved.

Aside from his children with Grimes, Musk is a father to nine other children with two other women. He and his first, ex-wife Justine Wilson welcomed six children. Their first, son Nevada Alexander, died at 10 weeks old in 2002.

The former spouses also share twins Vivian Jenna and Griffin, who were born in 2004, and triplets Kai, Saxon, and Damian, who were born in 2006.

Musk also has three children with Neuralink executive Shivon Zilis. They quietly welcomed twins in 2021 and confirmed the birth of their third child in June.

In September 2023, Grimes and Zilis made it clear there was no bad blood between them after Grimes previously addressed Zilis and her twins with Musk.

In an apology, Grimes wrote in part on X, “I spoke with Shivon at length finally, which was long overdue. This wasn’t her fault, plz don’t be angry at her! We respect each other a lot and we’re excited to become friends and have the kids grow up together.”

She continued, “Women are so often pitted against each other. Speaking with Shivon, it’s very evident she’s an amazing human and we both just want what’s best for our kids.”

Zilis responded on X, suggesting all is well between them.

“At the end of the day it all ended up for the best! Thank you for taking the time to really connect and understand each other. So glad we had such a wonderful talk, was insanely overdue. You’re a total badass and I respect you very much as well.”

She added that she couldn’t “wait” for a “kiddo play date” with Grimes’ and Musk’s children.

In May, Musk said he doesn’t plan on passing down his companies to his kids.

“I am definitely not of the school of automatically giving my kids some shares of the companies, even if they have no interest or inclination or ability to manage the company,” he revealed in an interview with The Wall Street Journal’s CEO Council. “I think that’s a mistake.”