A density-matrix theoretical model to calculate spectral line profiles of general multielectron ions in plasmas is described. The line-profile calculation involves electron collisional and radiative relaxation of ionic states, the emitter's motion (Doppler effect) and its interaction with a quasi-static ion microfield. Using the LineDM computer package implementing this model, line-profile calculations of the K- and L-shell transitions in Al XII, Ar XVII, Ar XVI, Cu XX, and Xe XLV ions have been performed in the context of plasma diagnostic issues of recent laboratory experiments. Comparisons of the calculated line profiles with experimental and other theoretical data show the applicability of the model and package for the detailed computational analysis of line radiation spectra from multielectron emitters in hot dense plasmas.