Fit multiple sub-ranges with TFractionFitter

  Dear all,

I would like to use TFractionFitter to fit multiple histograms at the same time: 5 Pt distributions corresponding to 5 different eta ranges

The histograms I have are the data distribution and 3 MC components (signal and 2 different backgrounds)
(note that the fit to each single Pt distribution is working fine)

A first solution I came up with is to create a new histogram with a size 5 times the single one and fill it with the 5 Pt distributions, placing them one next to the other (no sum!)

This is working as good as the single distribution fit but I now need to change the fitting range on each Pt distribution in order to avoid bin with low stats
Is it possible to fit multiple sub-ranges with TFractionFitter? If not, can you please suggest me another way of fitting multiple histograms at the same time with TFractionFitter?

Something I tried is to set the bin content(error) of the low stats bins to 0 but somehow TFractionFitter refills all these empty bins in order to have a more or less continuous distribution Perhaps this is perfectly normal and the reason explained in the full documentation, but I hadn't check it yet

Thanks,
s.