Statisticians are interested in improving the ability of classical distributions to appropriately fit real-world data and accurately describe its characteristics. Typically, this can be achieved by extending known distributions by incorporating extra parameters or compounding distributions. In this paper, a flexible general method to obtain new families of distributions is proposed. A number of known methods turn out to be special cases of the proposed method in this paper. Some examples are given to demonstrate the power of the proposed method such as the exponential and the Weibull distribution.