The former Zuma head chef will open his third site under the format later this autumn at the Bower development in Old Street.
He told M&C: "I am never going to be that guy who rolls out 100 restaurants around the UK; the doesn't excited me. But I think we could do ten in London and still maintain the quality."
He also hopes to eventually open a high end Japanese steakhouse - 100 covers, £80-100 spend per head - in the capital.
Last November he opened a second Bone Daddies site in Kensington within Whole Foods Market on the High Street to add to the first site in Soho on Peter Street, which opened in 2013.
Shonhan also operates Flesh & Buns in Covent Garden and a 12-month pop-up on Soho's Old Compton Street called Shackfuyu, which will become a permanent Bone Daddies after the initial year.
He would also like to launch a ready-filled bun takeaway version of Flesh & Buns in Soho, especially now awareness of buns generally is 'so much higher'.