In 2003, Bump-Friedberg-Ginzburg constructed the generalized global theta representation on a metaplectic double cover of an odd special orthogonal group. which was used later to construct the non-minimal theta liftings between double covers of orthogonal groups. This can be viewed as a generalization of the classical theta correspondence. In particular, it enjoys the tower property similar to the Rallis tower in the classical setting. This raises the question of when the first non-zero lifting will occur for a fixed theta tower. Bump-Friedberg-Ginzburg analyzed this problem when the automorphic representations are generic. In this talk, we will show the way to construct such theta liftings and talk about some progress towards understanding the non-generic cases.