Transfer learning (TL) has been demonstrated to improve DNN model performance when faced with a scarcity of training samples. However, the suitability of TL as a solution to reduce vulnerability of overfitted DNNs to privacy attacks is unexplored. A class of privacy attacks called membership inference attacks (MIAs) aim to determine whether a given sample belongs to the training dataset (member) or not (nonmember). We introduce Double-Dip, a systematic empirical study investigating the use of TL (Stage-1) combined with randomization (Stage-2) to thwart MIAs on overfitted DNNs without degrading classification accuracy. Our study examines the roles of shared feature space and parameter values between source and target models, number of frozen layers, and complexity of pretrained models. We evaluate Double-Dip on three (Target, Source) dataset paris: (i) (CIFAR-10, ImageNet), (ii) (GTSRB, ImageNet), (iii) (CelebA, VGGFace2). We consider four publicly available pretrained DNNs: (a) VGG-19, (b) ResNet-18, (c) Swin-T, and (d) FaceNet. Our experiments demonstrate that Stage-1 reduces adversary success while also significantly increasing classification accuracy of nonmembers against an adversary with either white-box or black-box DNN model access, attempting to carry out SOTA label-only MIAs. After Stage-2, success of an adversary carrying out a label-only MIA is further reduced to near 50%, bringing it closer to a random guess and showing the effectiveness of Double-Dip. Stage-2 of Double-Dip also achieves lower ASR and higher classification accuracy than regularization and differential privacy-based methods.