We extend the method of adaptive two-stage sequential sampling to include designs where there is more than one criteria is used in deciding on the allocation of additional sampling effort. These criteria, or conditions, can be a measure of the target population, or a measure of some related population. We develop Murthy estimator for the design that is unbiased estimators for the population mean, and propose another, more efficient, estimator. We investigate asymptotic properties of this estimator. We use a simulation study to investigate design properties of the multi-criteria adaptive sequential sampling scheme and also some estimator properties under the design.