The space astrometry mission Gaia will construct a dense optical QSO-based celestial reference frame. For consistency between optical and radio positions, it will be important to align the Gaia and VLBI frames with the highest accuracy. However, the number of quasars that are bright in optical wavelength (for the best position accuracy with Gaia), that have a compact core (to be detectable on VLBI scales), and that do not exhibit complex structures (to ensure a good astrometric quality), was found to be limited. It was hence realized that the densification of the list of such objects was necessary. Accordingly, we initiated a multi-step VLBI observational project, dedicated to finding additional suitable radio sources for aligning the two frames. The sample consists of ~450 optically-bright weak extragalactic radio sources, which have been selected by cross-correlating optical and radio catalogs. The initial observations, aimed at checking whether these sources are detectable with VLBI, and conducted with the European VLBI Network (EVN) in 2007, showed an excellent ~90% detection rate. The second step, dedicated to identify the most point-like sources of the sample, by imaging their VLBI structures, was initiated in 2008. About 25% of the detected targets were observed with the Global VLBI array (EVN+VLBA; Very Long Baseline Array) during a pilot imaging experiment, revealing that about 50% of them are point-like sources on VLBI scales. The rest of the sources were observed during three additional imaging experiments in March 2010, November 2010 and March 2011. The final stage was initiated in June 2012 with a first global observing experiment, dedicated to measuring accurately the VLBI position of the most point-like of such sources. In this paper, we present the results of the imaging campaigns and draw plans for the future.Read less <