Some people won't like it but here goes;
Modern take where Dante has pretty much sealed the door to the demon world permanently, and the world is at absolute peace; leaving Dante out of a job.
So we fast forward a couple of years to a Dante in his early 40's who's still in shape, and works as the owner of some convenient store or some small time job. Lady went on to be a hitwoman, while Trish became something of a traveler across the world. Patty is now the owner of a very profitable and loving orphanage, Morrison is Dante's drinking buddy, and Nero is back in Fortuna with Kyrie. Life has pretty much become something of normal for everyone.
However, Dante is bored of it all and wishes he could go back to what he use to. That all changes when a sudden Earthquake sends ripples across the planet and from the depths comes a heaping pile of defeated and killed demons from past DMC games. The origin is unknown, but Dante couldn't be more than happy to trade the manager vest for his red coat, and the price tag gun for his favorable ones.
And so the rest of the series is Dante traveling to different places around the world, with Lady, Trish, and Nero occasionally showing up.
A possible Vergil cameo down the road, some reference to past games (including DmC), and the obvious connection to Castlevania.