Studying SU(3) gauge theories with increasing number of fermions is relevant both for understanding the strong dynamics of QCD and for constructing strongly interacting extensions of the Standard Model (e.g. UV completions of composite Higgs models). In order to contrast these many-flavors strongly-interacting theories with QCD, we study the flavor-singlet spectrum as an interesting probe. In fact, some composite Higgs models require the Higgs boson to be the lightest flavor-singlet scalar in the spectrum of a strongly interacting new sector with a well defined hierarchy with the rest of the states. Moreover, introducing many light flavors at fixed number of colors can influence the dynamics of the lightest flavor-singlet pseudoscalar. I will present the on-going study of these flavor-singlet channels using multiple interpolating operators on high-statistics configurations generated by the LatKMI and the LSD collaboration. For the theory with 8 flavors, the two collaborations have generated configurations that complement each others with the aim to tackle the massless limit using the largest possible volumes. Results for $N_f=4,8$ and $12$ will be presented.