We extend the existing family of flexible survival models by assembling models scattered across the literature into a more knit form and under the same umbrella. New special cases are obtained not only by constraining the shape and scale parameters of the extended generalized gamma (EGG) model to fixed constants, but also by imposing relationships (such as equality, reciprocal, and negative reciprocal) between them. Apart from common parametric distributions such as exponential, Weibull, gamma, and log normal, the further extended family includes Rayleigh, inverse Rayleigh, ammag, inverse ammag, and half-normal distributions. The models are applied, in a Bayesian framework, on time to entry into first marriage among Eritrean men and women based on data from the 2010 Population and Health Survey. The application demonstrates that the further extended family of distributions provides a wide range of alternatives for a baseline distribution in the analysis of survival data. The empirical results reveal that the inverse gamma model fits best the data for men. It also performs closely as good as the EGG model in the data for women as well as in the combined sample.