In this paper, the sum of L independent but not necessarily identically distributed (i.n.i.d.) extended $η$-$μ$ variates is considered. In particular, novel expressions for the probability density function and cumulative distribution function are derived in closed-forms. The derived expressions are represented in two different forms, i.e., in terms of confluent multivariate hypergeometric function and general Fox's H-function. Subsequently, closed-form expressions for the outage probability and average symbol error rate are derived. Our analytical results are validated by some numerical and Monte-Carlo simulation results.