Interior characterization traditionally relies on individual planetary properties, ignoring correlations between different planets of the same system. For multiplanetary systems, planetary data are generally correlated. This is because the differential masses and radii are better constrained than absolute planetary masses and radii. We explore such correlations and data specific to the multiplanetary system of TRAPPIST-1 and study their value for our understanding of planet interiors. Furthermore, we demonstrate that the rocky interior of planets in a multiplanetary system can be preferentially probed by studying the densest planet representing a rocky interior analog. Our methodology includes a Bayesian inference analysis that uses a Markov chain Monte Carlo scheme. Our interior estimates account for the anticipated variability in the compositions and layer thicknesses of core, mantle, water oceans, and ice layers, as well as a gas envelope. Our results show that (1) interior estimates significantly depend on available abundance proxies and (2) the importance of interdependent planetary data for interior characterization is comparable to changes in data precision by 30%. For the interiors of TRAPPIST-1 planets, we find that possible water mass fractions generally range from 0% to 25%. The lack of a clear trend of water budgets with orbital period or planet mass challenges possible formation scenarios. While our estimates change relatively little with data precision, they critically depend on data accuracy. If planetary masses varied within ±24%, interiors would be consistent with uniform (~7%) or an increasing water mass fractions with orbital period (~2%–12%).