The investor bought the 450-store chain less than a year ago, rebranding it from the well-known WH Smith to TG Jones.
The new proposals include as many as 150 store closures, as well as landlords of some remaining stores receiving no rent whatsoever.
Modella has warned court approval is needed for the plan by the end of June, or TG Jones will go into administration.
Willson, who took over the role in April, said he was initially greeted with a “huge scale of under-investment” in the business, noting some stores were missing lightbulbs and ceiling tiles, had threadbare carpets, and had lifts and escalators that didn’t work.
He added that it was “bonkers” that some stores were run by a single employee.
Modella has previously said it bought retailers in need of “significant investment” in the hopes of returning them to sustainable growth, but conceded that it won’t “win every battle”.