  Precise millisecond pulsar (MSP) positions determined with very long baseline
interferometry (VLBI) hold the key to building the connection between the
kinematic and dynamic reference frames respectively used by VLBI and pulsar
timing. The frame connection would provide an important pathway to examining
the planetary ephemerides used in pulsar timing, and potentially enhancing the
sensitivities of pulsar timing arrays used to detect stochastic
gravitational-wave background at nano-Hz regime. We aim at significantly
improving the VLBI-based MSP position from its current $\gtrsim1\,$mas
precision level by reducing the two dominant components in the positional
uncertainty -- the propagation-related uncertainty and the uncertainty
resulting from the frequency-dependent core shifts of the reference sources. We
introduce a new differential astrometry strategy of using multiple calibrators
observed at several widely separated frequencies, which we call PINPT
(Phase-screen Interpolation plus frequeNcy-dePendent core shifT correction;
read as "pinpoint") for brevity. The strategy allows determination of the
core-shift and mitigates the impact of residual delay in the atmosphere. We
implemented the strategy on PSR J2222-0137, an MSP well constrained
astrometrically with VLBI and pulsar timing. Using the PINPT strategy, we
determined core shifts for 4 AGNs around PSR J2222-0137, and derived a
VLBI-based pulsar position with uncertainty of 0.17 mas and 0.32 mas in right
ascension and declination, respectively, approaching the uncertainty level of
the best-determined timing-based MSP positions. The realization of the PINPT
strategy promises a factor-of-5 positional precision enhancement (over
conventional VLBI astrometry) for all kinds of compact radio sources observed
at $\lesssim2$ GHz, including most fast radio bursts.
