Wirral residents are being asked how the council can save an extra £27.5m in the next year.
A public consultation will be held until December, with roadshows taking place in the next week.
The authority was expected to have to save £109m - or about a third of its budget - over the next three years but says extra cuts are now needed.
"Extremely tough" decisions will have to be made, the council's chief executive Graham Burgess said.
One proposal is to close one of three Wirral day care centres for adults with disabilities.
In August most of the council's 4,700 staff took the first of four days' unpaid leave to save up to £1.5m.
In June the council brought in charges of £35 a year to have garden waste bins emptied every fortnight and in April it introduced an extra charge for cremations of larger coffins.
The authority announced in March that it needed to cut 350 posts to save costs.
Plans to merge the administration services of Liverpool, Halton, Knowsley, Sefton, St Helens and Wirral councils are also being discussed.
A spokesman said a similar consultation last year contributed to savings of almost £50m being made, including efficiencies in areas such as administration, marketing, agency costs, car mileage and phone bills.
Mr Burgess said: "We have more extremely tough decisions to make over the coming months and the only way that we can do this is in partnership with Wirral people.
"Our duty as public servants is to do all we can to use the limited resources we have left in the most effective way possible to continue to ensure the services that people rely on most remain available in some form."