In the last three years, the migrativity of triangular norms \((T(a,x,y)= T(x,a,y))\) for a fixed \(a\) was extensively studied and generalized in different directions. In this paper, a generalized form of migrativity equation is studied \[ (T(T_0(a,x), y)= T(x,T_0(a,y))) \] for particular cases when \(T_0\) is the strongest t-norm \(T_M\) or the Łukasiewicz t-norm \(T_L\), and \(T\) is a continuous t-norm. The authors have characterized all possible solutions \(T\) in the above-mentioned cases. By isomorphism the case when \(T_0\) is a nilpotent t-norm is covered, too.