I already know about the classical Central Limit Theorem (CLT):
Let $X_1, \dots , X_n \in \mathbb{R}^d$ be the iid random variables drawn from a distribution with mean $\mu$ and covariance matrix $\Sigma$. Let $\displaystyle \bar{X} = \frac{1}{n} \sum_{i = 1}^{n}{X_i}$ Then, $$\sqrt{n}(\bar{X} - \mu) \rightsquigarrow \mathcal{N}(0, \Sigma). $$
But if we change the condition as $X_1, \dots, X_n \in \mathbb{R}^d$ are independent RVs but not identically distributed, the classical CLT result will not hold.
My question is: For the multivariate independent but not identical RVs, does there exist any CLT (like the classical one) for them but without the triangular array assumption?