The radio and gamma-ray pulsar PSR J2032+4127 was recently found to be in a decades-long orbit with the Be star MT91 213, with the pulsar moving rapidly towards periastron. This binary shares many similar characteristics with the previously unique binary system PSR B1259-63/LS 2883. Here, we describe radio, X-ray, and optical monitoring of PSR J2032+4127/MT91 213. Our extended orbital phase coverage in radio, supplemented with Fermi gamma-ray data, allows us to update and refine the orbital period to 45-50 yr and time of periastron passage to 2017 November. We analyse archival and recent Chandra and Swift observations and show that PSR J2032+4127/MT91 213 is now brighter in X-rays by a factor of ~70 since 2002 and ~20 since 2010. While the pulsar is still far from periastron, this increase in X-rays is possibly due to collisions between pulsar and Be star winds. Optical observations of the Halpha emission line of the Be star suggest that the size of its circumstellar disc may be varying by ~2 over timescales as short as 1-2 months. Multiwavelength monitoring of PSR J2032+4127/MT91 213 will continue through periastron passage, and the system should present an interesting test case and comparison to PSR B1259-63/LS 2883.