Filter data dynamically based on customized calendar on a particular visual only

Hi,

I came across a requirement from my client that the data must change every month on a particular visual on first of every month, but the date on which it should update next month's data is not based on the regular calendar but is based on a particular calendar that their company follows. 

The "Filter on the visual" option does not work fine for this particular scenario since the functionality works based on the regular calendar (It updates data on the first of every month). 

The choice of filtering data with the help of a slicer for month and year is eliminated (since it shows historical data as well).

So now, how do I update the data based on their calendar? Is it possible to make this requirement work on PowerBI?

Thanks in advance.