yes, it is possible. it is enough to find the meaning of direct and indirect band gaps which both can be presented in a material. however, there is a prefered condition for that. that is why some materials have direct and some other ones have indirect band gap.
a typical bandstructure E(k) is shown in the attachement. The number of minima depend on the E(k)-structure. These minima exist in the momentum space k and not in the local space . In dependence of your investigation method (I assume optical methods) different extrema can determine the result of investigation. But it would be necessary to know, what you observed before a detailed answer can be given.
My material is alkaline earth metal based chalcogenide. Using Tauc plot, Direct band gap is coming around 1.3 eV and indirect band gap is 0.69 eV. We have used solid state UV/VIS/NIR spectrometer having range 200 nm to 1500 nm.
The references mentioned in the following link might give some answers https://www.researchgate.net/post/What_is_the_best_experimental_method_for_calculating_of_the_band_gap_of_a_semiconductor_material_what_is_it_based_on