Questions about new game plus for DMC1

[Kiribri]

Hello, from what I've read so far the difficulties are Normal -> Hard (both pre-selected for you) and then you get the difficulty choice after you beat Hard while also unlocking Dante Must Die.

Is it possible to do another playthrough after Dante Must Die on Normal? Or if I do a Normal playthrough after Hard, can I start Dante Must Die after my second Normal?

I am asking this to collect some missing files and do some secret missions I've missed (and maybe even the no death run achievement), I would like to do them on Normal.

[Director Bison]

Beating Hard unlocks choosing your NG+ permanently, regardless of Difficulty or if it's a brand new save. So yes if you beat DMD you can go back to Normal if you want.

[Kiribri]

Thanks