Studying planetary interactions in exoplanet systems informs theories of planet formation and evolution, providing essential context for understanding our own solar system. We combine spectroscopy, transit photometry, transit timing variations, and astrometry to characterize the TOI-201 system. The cotransiting system consists of a super-Earth, warm Jupiter, and massive companion at 5.8-, 53-, and 2900-day orbital periods, respectively. We perform dynamical simulations to study the past and future of the system. von-Zeipel-Kozai-Lidov oscillations emerge as the most plausible scenario to explain the outer companion's high orbital eccentricity, with planet-planet scattering a possible but less likely contender. Because of nonzero mutual inclinations between the planets, the system is visibly evolving on very short timescales, with the current cotransiting configuration ending in 200 years.