Very Long Baseline Interferometry (VLBI) is the only technique that connects the celestial and the terrestrial reference frames. Because of its essential role, it is important to investigate the quality of VLBI observations and their effect on the estimated parameters. The fundamental goal of the quality assessment using the sensitivity is to find out to what level VLBI can detect station displacements in the adjusted coordinates. However, the global VLBI station network is worse in terms of the number and global distribution of stations when compared to the GNSS station network. In this study, we aim to improve the capacity of VLBI to detect station displacements through an inter-technique combination with GNSS. The effect of the selection of co-location sites in the inter-technique combination is investigated with four scenarios and we investigate how the sensitivity is affected by the assumed standard deviations of the local ties. The lower the standard deviations of the local ties, the higher the obtained sensitivity level. When larger standard deviations are assumed, the sensitivity levels of the VLBI stations are obtained up to 3 mm. When a smaller deviation is assumed for a local tie having various standard deviations obtained from different local tie observations, the sensitivity levels change too. If local ties with standard deviations of 1 cm and more are excluded, the detection capacities of the VLBI stations based on the gross errors improve by around 1 mm. When smaller standard deviations are assumed among the local ties, which are used in the inter-technique combination, the sensitivity levels drop below 2 mm. Hence, this study quantifies how important the selection of the co-location sites and the standard deviations of the local ties are for the accuracy of geodetic products obtained by inter-technique combination.