I was thinking about how to involve the girls a bit more, and figured that you could potentially solve a few problems by introducing a character like Phaser Ryugu into DMC6.
For those of you who aren't into children's card games, Phaser is a human who absolutely hates aliens (in a G-rated form of racism kind of way) and both founded and commands the MIK (a parody of the Men in Black) which is dedicated to monitoring and countering the aliens who have infiltrated Japan and are posing as humans.
Considering the monumental shift in setting during the events of DMC5 whereby the apocalypse basically happened and humanity became irreversibly aware of the existence of demons, it makes total sense that every country would dedicate resources to creating an anti-demon force. You then introduce the face of this anti-demon organisation through a Government Demon Slayer who acts as a foil to Lady in that this person lost family members to demons and has an intense prejudice to anyone loosely affiliated with demons. Therefore he naturally targets Trish and is interested in capturing Nero because of his demonic heritage.
How this character ends up could go a variety of different ways, but I would be most interested in seeing him challenge Trish philosophically on some of the conventions in the franchise, like what is the line of logic that permits her to freely hunt and kill demons (as we see her do in DMC4) when she herself is one. Ultimately I think it would be preferable for such a character to resist becoming a straight up hero through redemption, considering the sheer threat that demons have been shown to pose, he should either die an antagonist or learn to tolerate the heroes' existence as a necessary evil but will hunt them down if they put a toe out of line.
This was a bit of a ramble, but I think it goes to show that despite DMC5 feeling like it could have ended the series, there's still paths open if you think of interesting ways to connect the dots.