The sequencing of reactants and reaction parameters in the two-stage coprocessing of coal with low-density polyethylene (LDPE) and petroleum resid was investigated using two fractional factorial designs and analyses of variance(ANOVA). The experiments were designed to determine the sequence of reactants and the reaction conditions that were required to achieve the highest level of conversion of the solid reactants, and to achieve a desirable product slate in terms of product solubility and boiling point distribution. The reaction system that yielded the highest amount of hexane solubles regardless of the reaction temperature sequence or extraction after the first stage was the catalytic Liquefaction of LDPE in the first stage, with the reaction products being added to coal and heavy resid in the second stage, which was also reacted catalytically. Examination of the effect of coal content and H-2 pressure in the first and second stages showed that the Ka pressure affected the amount of coal conversion achieved. A higher level of coal content, 28% compared to 5%, resulted in higher coal conversion. Lower Ha pressure in both stages resulted in higher LDPE conversion, but adversely affected coal conversion, particularly at low coal concentrations.