We develop a novel method for finding sufficient experimental conditions for discriminating and quantifying individual biomolecule production sources in distributed, inhomogeneous multisource systems in vivo, and we apply it experimentally to a complex, unsolved problem in endocrinology. The majority of hormonal triiodothyronine (T3) is produced from prohormone thyroxine (T4) in numerous nonthyroidal organs and, with one exception, the T3 production rate has not been fully resolved in any single extrathyroidal organ of any species. Using a readily generalized graphic method called cut-set analysis, we show here that measured steady-state responses in several organs to three independent tracer infusions, two into blood and one directly into the organ(s) of interest, are sufficient to resolve this problem for organs fully accessible to direct infusion in vivo. We evaluated local T3 production in rat liver and intestine, which also required T3 bile flux measurements, and we found that liver produces approximately 31% and whole intestine approximately 6% of whole body T3 from T4. With thyroidal production included, liver contributes approximately 15% and intestine approximately 3% of whole rat T3 production. This new methodology is broadly applicable, especially to biosystems that include molecular interconversions at multiple sites.