Subsampling can be used in experimental design to investigate extraneous sources of variability. One useful strategy is to make independent replicate measurements of the response variate. This can be achieved in clinical studies, for example,by dividing a blood or urine specimen from each of a sample of subjects into aliquots and processing these through a chemistry laboratory in such a way that the replicate determinations are independent. This procedure can be used to increase design efficiency. This paper addresses considerations in the design and analysis of the 2×2 crossover plan with this type of subsampling.