Collision-induced vibrational energy transfer has been studied from two vibrational levels at intermediate state density in S-1 p-difluorobenzene in a supersonic free jet expansion at similar to 30-40 K. Transfer was studied from the 7(1)8(1) (E-vib=751 cm(-1)) and 8(4) (E-vib=733 cm(-1)) states where rho(vib) is similar to 0.4 states per cm(-1). Data were obtained for He, Ne, H-2, and D-2 for both levels and also for Ar and Kr for 7(1)8(1). There is some doubt concerning the influence of predissociation of van der Waals complexes on the spectra for these latter partners. The data analysis for 7(1)8(1) is quantitative for all collision partners. For 8(4) the analysis is quantitative for H-2 and D-2 but qualitative for He and Ne because of poor signal levels. The state-to-state propensity rules in this region of the vibrational manifold are compared with those observed at lower state densities, particularly those from 8(2). The main feature to emerge is a lack of predictability of the major relaxation pathways. There is a clear increase in the importance of transfers involving multiple changes in vibrational quanta for all situations studied and at times such transfers totally dominate. This occurs in spite of the possibility for loss of one quantum of nu(8), which is a very efficient channel in transfer from 8(2). Collision partners that show similar state-to-state branching ratios for 8(2) show quite different branching ratios for 7(1)8(1) and for 8(4).