You will not get much "bit" into 3/8" ply. for the new 3/4". Might be better to remove some of that 3/8", add blocking, put it back, then install the new sub.
Normally the new top ply (underlayment) is fastened only into the subfloor. In this case you should pretend the 3/8" is not there, except I would still add some screws between the joists.
Don't forget the thin set mortar under the concrete backer, tape joints etc.
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