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Multi-part Balanced Incomplete Block Designs is a combination of many orthogonal balanced incomplete block designs in the same block. The design has been used to study cancer trials with medical centers as blocks. Various design layouts has been constructed for a restricted number of cancer types and drugs. However, parameter estimation, hypothesis testing, and model building for the constructed design layouts have not being considered. Based on the foregoing, we proposed additive model for the design (2-part Balanced Incomplete Block Designs) and estimated its parameters using the least square method. The parameter estimation precipitated to the formation of ANOVA table which paved way for the hypothesis testing procedure.