Climate change can drive local climates outside the range of their historical year-to-year variability, straining the adaptive capacity of ecological and human communities. We demonstrate that dependencies between climate variables can produce larger and earlier departures from natural variability than is detectable in individual variables. Using the example of summer temperature (Tx) and precipitation (Pr), we show that this departure intensification effect occurs when the bivariate climate change trajectory is misaligned with the dominant mode of joint historical variability. Departure intensification is evident in all six CMIP5 models that we examined: 23% (9-34%) of the global land area of each model exhibits a pronounced increase in 2σ anomalies in the Tx-Pr regime relative to Tx or Pr alone. Observational data suggest that summer Tx-Pr correlations in distinct regions on all continents are sufficient to produce departure intensification. Precipitation can be an important driver of multivariate climate change signals relative to natural variability, despite typically having a much weaker univariate signal than temperature.