The theory of Part I is extended to problems in which it is permitted not to come to a definite conclusion regarding one or more of the questions under consideration. Some problems are also investigated in which, from a single set of observations, one wishes to answer a number of questions in sequence. Here the nature of the question at a later stage will depend on the answers obtained at the earlier stages.
E. L. Lehmann. "A Theory of Some Multiple Decision Problems. II." Ann. Math. Statist. 28 (3) 547 - 572, September, 1957. https://doi.org/10.1214/aoms/1177706873