This work is a study of the influence of shell effects on the formation of binary fragments in damped collision. We have investigated binary reaction channels of the composite system with $Z=108$ produced in the reaction $^{88}\mathrm{Sr}$${+}^{176}$Yb at an energy slightly above the Bass barrier (${E}_{\text{c.m.}}/{E}_{\text{Bass}}=1.03$). Reaction products were detected by using the two-arm time-of-flight spectrometer CORSET at the K130 cyclotron of the Department of Physics, University of Jyv\"askyl\"a. The mass-energy distribution of primary binary fragments has been measured. For targetlike fragments heavier than 190 u, which correspond to a mass transfer as large as twenty nucleons or more, an enhancement of the yields is observed. This striking result can be ascribed to the proton shells at $Z=28$ and 82 and implies the persistence of the shell effects in the formation of reaction fragments even for large mass transfers.