Design storms are key components for planning drainage networks and flood risk management. Due to atmospheric processes, precipitation accumulations across multiple temporal intervals are often correlated and can combine to shape flood intensities. However, current design storm guidance overlook the observed correlations between return periods of different duration intervals within storms and may thereby lead to under- or over-estimation of the flood risk. We present a new approach for generating plausible design storms that accounts for joint return periods. Focusing on short-duration extreme precipitation events, potentially leading to urban pluvial flooding, we analyze the dependencies between critical precipitation intensities over the 10-min, 30-min, 1-hr, 3-hr, and 6-hr intervals, for data from Zurich (Switzerland). We then propose a method based on a canonical vine copula model for sampling precipitation intensities that reflect the observations' dependencies. Using this model, we then generate realistic design storms with a constrained micro-canonical cascade model. Our results shows that the common block methods (e.g., the Chicago and Euler design storms) tend to overestimate total precipitation volumes on average, by up to 56%. Furthermore, we highlight the variability in possible duration-frequency profiles, leading to both higher and lower total precipitation volumes compared to standard approaches. This underscores the need to switch from traditional block methods to a more realistic sampling of design storms, incorporating multiple design storm scenarios for robust risk assessment. The model is applicable to any time series of precipitation, regardless of its location or climate. The code is freely available.