Intense heavy ion beam production with electron cyclotron resonance (ECR) ion sources is a common requirement for many of the accelerators under construction in Europe and elsewhere. An average increase of about one order of magnitude per decade in the performance of ECR ion sources was obtained up to now since the time of pioneering experiment of R. Geller at CEA, Grenoble, and this trend is not deemed to get the saturation at least in the next decade, according to the increased availability of powerful magnets and microwave generators. Electron density above 10(13) cm(-3) and very high current of multiply charged ions are expected with the use of 28 GHz microwave heating and of an adequate plasma trap, with a B-minimum shape, according to the high B mode concept [S. Gammino and G. Ciavola, Plasma Sources Sci. Technol. 5, 19 (1996)]. The MS-ECRIS ion source has been designed following this concept and its construction is underway at GSI, Darmstadt. The project is the result of the cooperation of nine European institutions with the partial funding of EU through the sixth Framework Programme. The contribution of different institutions has permitted to build in 2006-2007 each component at high level of expertise. The description of the major components will be given in the following with a view on the planning of the assembly and commissioning phase to be carried out in fall 2007. An outline of the experiments to be done with the MS-ECRIS source in the next two years will be presented.