We present a theoretical quasiclassical study of the formation, during Coulomb explosion, of two highly excited neutral H atoms (double H$^{*}$) of strongly driven H$_2$. In this process, after the laser field is turned off each electron occupies a Rydberg state of an H atom. We show that two-electron effects are important in order to correctly account for double H$^{*}$ formation. We find that the route to forming two H$^{*}$ atoms is similar to pathway B that was identified in Phys. Rev. A {bf 85} 011402 (R) as one of the two routes leading to single H$^{*}$ formation. However, instead of one ionization step being frustrated as is the case for pathway B, both ionization steps are frustrated in double H$^{*}$ formation. Moreover, we compute the screened nuclear charge that drives the explosion of the nuclei during double H$^{*}$ formation.
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