NEXP = Σ$_2$ ⟹ NEXP = MA? Is it known whether the implication $\mathsf{NEXP} = \Sigma_2 \implies \mathsf{NEXP} = \mathsf{MA}$ holds?

(The question is inspired by well-known $\mathsf{NEXP} \subseteq \mathsf{P/poly} \Leftrightarrow \mathsf{NEXP} = \mathsf{MA}$.)
This is not known. 

$NEXP = \Sigma_{2}$ means that $NP$ and $NP^{NP}$ are different. But, $MA$ seems too weak to reach that high to catch $NP^{NP}$.