The buffet brand, which serves around 150 dishes at low prices, shut its Coventry site on 7 March after 15 years of trading.
A note on its Facebook page blamed the “well documented pressures on our industry and tough trading conditions”.
Its York restaurant closed on 15 March and has now reopened under buffet brand Panda Mami, which also has a site in Chester.
Cosmo, which says it is inspired by the food offering at some of "the best five-star hotels in the world", launched in the UK in 2003 and currently runs 19 sites across the country.
The group attempted to go high-end in 2017 by relaunching its Leeds site under the more upmarket Cosmo Luxe concept. It was intended as a possible template for a new brand with a more "elegant" design and "gourmet" dishes.
A note on the Leeds restaurant’s website says it is currently closed due to "unforeseen technical issues".