We study a drift-diffusion system on bounded domain in two-spacedimension. This model is provided with a hetero-separative andhomo-aggregative feature subject to a gradient of physical orchemical potential which is proportional to their densities. Weextend a criterion of global-in-time existence of the solution,especially for non-radially symmetric case. Then we perform theblowup analysis such as the formation of collapses and collapsemass separations. A slightly different model describing crosschemotaxis is also discussed.