Gaius Danius Griinia
Apparently Infamous
I did want a thing between Rinzler and IzuruGaius Danius Griinia Alright, sure. So he's power-hungry, unstable, and enjoys eating monsters. A little basic but, hey, simple is best. Now the idea is you take these traits and extrapolate them outwards and expand upon them a little, flesh your guy out. Maybe use this to inform a dynamic. Reach out and touch somebody, you know?
For example: You wanted to have a thing going with Amaya Himura , right? So say, hypothetically, maybe the Rinzler family aren't just some big-dick court assassins/manservants/whatever. Maybe that's just their day-to-day, and their real purpose is to hold the Emperor in check and cut him down should he descend into full-blown crazy, since that's a thing demigods do here. This, then, could give Amaya Himura an in for a character arc about how the previous Rinzler failed in their duty to assassinate the king and how she feels somehow at fault for the empire being such a mess right now. See how that organically emerges? Now, keep in mind, I'm not actually saying YES DO THIS SPECIFIC STORYLINE. It's just an example of what you and another person could do working with the traits you've listed.
The important thing here is that, now that you've established these things, you actually try to use them to inform your character a little. This doesn't mean you have to rave like a lunatic + eat a monster + kill someone for a magic item every post. It just means that, say, if your character was presented with the opportunity of chowing down on a monster carcass, he would at very least put some serious consideration towards doing so. Make sense?
Though now theres Yuki and Emlyn so we have enough Waifus for now
I can adapt that... instead of assassinating the Emperor
How about just keeping him from giving into his demented instincts?
Though I do like Old Man Rinzler failing to kill Izaya when he went too far