The group is currently working with property agency Stonebrook London to help identify perspective locations for expansion for the all-day concept.
Founders Gemma and Mike Simmonite are specifically concentrating on ABC1 sites in the UK, and presently in talks to acquire a spot in Cambridge.
Future target locations include Brighton, Oxford, Cheltenham, Reading, Bath and Cardiff.
The founders say they are looking for areas with an abundance of retail, plus a prosperous evening trade to suit their 'all-through neighbourhood restaurant style'.
Gastrono-me's current restaurant on Abbeygate Street in Bury St Edmunds, Suffolk, was opened by Gemma and Mike back in 2015.
The 108-cover site, which is currently closed as a result of England's ongoing lockdown restrictions, serves induvial breakfast, brunch and dinner menus that revolve throughout the day.
Dishes from the dinner menu include the Korean-style brisket sandwich; deep-fried burrata served with marinara sauce and garlic bread; and tempura beer-battered avocado tacos served with a fresh corn salsa, lettuce, pink-pickled onions and chipotle crema.
Bottomless brunch and bottomless dinner options are also available on specific days throughout the week.
The restaurant also houses an underground speakeasy style karaoke room which has proven immensely popular with parties and private functions.
Gastrono-me's expansion is backed by private equity.