Various methods of introducing additional parameter to a family of multivariate exponential and Weibull distributions are presented. One of them is used to give a new two-parameter extension of the multivariate exponential distribution which may appear to be easier to deal with than those such commonly used two-parameter family of multivariate life distributions as the Weibull, gamma and log-normal distributions. Another general method that allows additional new three-parameter to a family of multivariate Weibull distribution is also introduced and studied. All the families of distributions expanded by either or both of these methods have the property that the minimum of a geometric number of independent random variables with common distribution in the family has a distribution also in the family.