Simultaneous or near-simultaneous observations at multiple frequency bands have the potential to overcome the fundamental limitation imposed by the atmospheric propagation in mm-VLBI observations. The propagation effects place a severe limit in the sensitivity achievable in mm-VLBI, reducing the time over which the signals can be coherently combined, and preventing the use of phase referencing and astrometric measurements. We present two demonstrations of the power of (near) simultaneous multi-frequency observations with the KVN and VLBA, and our recently developed analysis strategies to enable new measurements at mm-VLBI. The first case comprises simultaneous observations at 22, 43, 87 and 130 GHz of a group of five AGNs, the weakest of which is ∼200 mJy at 130 GHz, with angular separations ranging from 3.6 to 11 degrees, using the KVN. We analysed this data using the Frequency Phase Transfer (FPT) and the Source Frequency Phase Referencing (SFPR) techniques, which use the observations at a lower frequency to correct those at a higher frequency. The results of the analysis provide an empirical demonstration of the increase in the coherence times at 130 GHz from a few tens of seconds to about twenty minutes, with FPT, and up to many hours with SFPR. Moreover the astrometric analysis provides high precision relative position measurements between two frequencies, including, for the first time, astrometry at 130 GHz. The second case is a variation of the above, whereby adding dedicated wide-band cm-wavelength observations to measure the ionosphere eliminates the need for a second, calibrator, source. This addresses the scarcity of calibrators at mm-VLBI. We dubbed this technique Multi Frequency Phase Referencing (MFPR). We present bona fide astrometrically aligned VLBA images of BL Lacertae at 22 and 43 GHz using MFPR, which, combined with results from conventional phase referencing at cm-wavelengths, suggests the VLBI core has a recollimation shock that is revealed at mm-wavelengths. These shocks could be responsible for the γ-ray emission in blazar jets.