We report on the first global high-precision (differential phase-delay) astrometric analyses performed on a complete set of radio sources. We have observed the S5 polar cap sample, consisting of 13 quasars and BL Lac objects, with the VLBA at 8.4, 15, and 43 GHz. We have developed new algorithms to enable the use of the differential phase-delay observable in global astrometric observations. From our global analyses, we determine the relative positions between all pairs of sources with typical precisions ranging from 10 to 200 μas, depending on observing frequency and source separation. In this paper, we discuss the impact of this observable in the enhancement of the astrometric precision. Since a large fraction of the S5 polar cap sources are ICRF defining sources, this may result in a test of the ICRF stability. Our multi-epoch/multi-frequency approach will also provide both absolute kinematics and spectral information of all sources in the sample. In turn, this will provide an important check on key predictions of the standard jet interaction model.