The onset of convective instability is analysed in a rotating ulticomponent fluid layer in which density depends on n stratifying agents (one of them is heat) having different diffusivities. Two problems have been analysed mathematically. In the first problem, a sufficient condition is derived for the validity of the principle of the exchange of stabilities. Further, when the complement of this condition holds good, oscillatory motions of neutral or growing amplitude can exist, and thus it is important to derive upper bounds for the complex growth rate of such motions when at least one of the bounding surfaces is rigid so that exact solutions of the problem in closed form are not obtainable. Thus, as the second problem, bounds for the complex growth rates are also obtained. Above results are uniformly valid for quite general nature of the bounding surfaces.