Four Seasons, which has 20,000 elderly residents across 450 homes, said earnings were up by 40% to £19.7m in the third quarter as occupancy rose to 89.6%, the highest level in more than three years.
However, the company's £525m debts and annual £50m interest payments continue to be a concern.
The group, owned by financier Guy Hands' private equity vehicle Terra Firma, admitted in April that it did not have enough money to meet its long-term needs, adding that it was exploring its options.
The options thought to be under consideration include refinancing the debt, a sale or a debt-for-equity swap with lenders - where borrowings are waived in exchange for control of a company.
It is understood that Hands is also considering pumping fresh equity into the company.
Four Seasons chairman Robbie Barr said that the Terra Firma is in "active discussions" to find a long-term solution for the group's debt and capital structure.
Barr added: "We have continued to build on the turnaround and the positive momentum that we achieved in the first half of 2016.
“Occupancy in our homes is up again, underpinned by our continuing improvements in quality of care; our revenues are up and EBITDA (earnings) is up."
The company, which has been stung by a cut in local authority fees and rising costs such as the National Living Wage, again urged the government to devise a long-term plan for funding social care.
"It remains critical that the government considers the longer term strategy for the funding of social care in order to try to deal with the inequities that exist and to bring some stability to the future of social care-funded services," it said.
The results come as experts warn of a full-blown crisis in social care.
A report by restructuring specialist Opus Business Services shows that a raft of major financial problems are affecting care home operators which "at best will lead to compromises in care standards and, at worst, threatens a significant number of homes with closure or new ownership".
Using data compiled by corporate health monitor Company Watch, Opus found that about 6,000 care homes could need financial rescue within the next three years to avoid being closed.
Nick Hood, business risk adviser at Opus, said: "Every part of the UK adult care system is in crisis.
"Our research shows that far too many operators face a serious risk of failure and a deeply worrying number are in negative financial equity. Debt levels for those who borrow are far too high.
"In the Autumn Statement, the government missed its chance to tackle the residential care crisis and restore the £2bn funding it took away to help plug its deficit.
“Right now, the UK is sleepwalking into a full-blown residential care crisis."