As reported in https://root.cern.ch/phpBB3/viewtopic.php?f=15&t=22635, a non-extended likelihood fit returns a wrong result when fitting multiple ranges.
The extended maximum likelihood fit with RooFit returns a correct result.
A simple test program is attached where a polynomial fit of two sidebands is performed.
As comparison an extended and non extended likelihood fit using directly ROOT is performed.
(running the ROOT fit requires using the master for a bug fix in the extended maximum likelihood fits).