Welcome to the forum and welcome to the fandom.
As it stands, a fourth volume sadly hasn't been solicited. The second half of the book as a whole isn't nearly as good as the Puckett/Scott run, but there are plenty of amazing issues and major highlights for you to look forward to.
Mind sharing? That sounds adorable.
Were I given a solo spinning out of 'Tec, I have a pretty clear general idea about how I'd handle it. A few arcs in, I'd have 'Basil' pop up before Cass during a patrol, in complete control of himself but with no memory of how he came back, the two going on to spend a brief period together, having a good time. it'd soon be revealed that 'Basil' was actually one of the other Clayfaces in disguise, having seen old news video footage of Cass and Basil fighting together in the field and attempting to get to Batman through her. At the moment he thinks he's been brought to Batman's HQ, mocking Cass and how easy it was to fool her, it'd be revealed that she lead him into a trap, freezing him, and tearfully revealing that she knew he wasn't real all along from his body language. She just wanted to pretend for a bit.
Sometime later, the actual Basil would come back, but the Clayface personality would have complete control and it would have an obsession with hurting Cass. He'd spend time as the big bad of the book, popping in and out of focus, with Cass still wanting to save him no matter how many different ways he hurts her (sort of like Angelus in season 2 of Buffy, but with a more general toxic relationship theme as opposed to the abusive boyfriend story done there). The storyline would end with Cass managing to cure Basil with assistance from other BatFam members and since he's already legally dead they're able to avoid the legal system, but Basil would be completely traumatized from being in the backseat during all of Clayface's monstrous actions. He'd join the supporting cast, initially as a figure for Cass to help someone else through their trauma, the way he was there for her in this continuity, and ultimately getting his life back together in a new identity.