Collaborative filtering (CF) systems are widely used by many e-commerce sites. However, they fail to provide privacy measures. That is why it becomes a challenge to collect truthful and dependable data to perform CF services. Researches show that privacy concerns differ from user to user. Therefore, users might decide to hide their private data differently. Providing CF services on variably masked data is challenging. Two parties may need to combine their data for CF purposes for better recommendations. However, they do not want to integrate them due to privacy, legal, and financial reasons. If privacy measures are provided, they can combine their data. The challenge is then how they can offer CF services on integrated data without violating their privacy. In this study, solutions are proposed to overcome each of the abovementioned challenges. The proposed schemes are analyzed in terms of accuracy, privacy, and additional costs. After explaining the solutions, conclusions are drawn and future directions are presented.